Operable invasive breast cancer Invasive lobular cancer Concurrent diagnosis of invasive or microinvasive breast cancer in either breast Subjects must have histologically confirmed invasive breast cancer and registration must occur within 12 months after the first histologic diagnosis of invasive breast cancer\r\n* A core biopsy interpreted as invasive cancer meets this criterion; if no core biopsy is performed, the date of first histologic diagnosis will be the date of first surgical procedure that identifies invasive cancer (biopsy, lumpectomy or mastectomy)\r\n* Neoadjuvant subjects should have no evidence of clinical T4 disease prior to chemotherapy and surgery; eligibility for neoadjuvant patients can be defined by either clinical stage prior to therapy or pathologic stage at surgery; if patient is eligible based on either, they are eligible for the study\r\n* Bilateral breast carcinoma is allowed provided either:\r\n** Diagnoses are synchronous – that is, within 3 months of one another – and at least one of the two breast carcinomas meet the eligibility criteria and neither is Her-2 positive or inflammatory; OR\r\n** The contralateral breast cancer was at least 5 years prior to the current diagnosis\r\n* No evidence of metastatic disease Patients must not have metastatic breast cancer (stage IV disease); patients with multifocal, multicentric, and synchronous bilateral, and primary inflammatory breast cancers are allowed\r\n* Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant\r\n* Multicentric disease is defined as more than one invasive cancer >= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants\r\n* Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other; (NOTE: the tumor with the highest recurrence score should be used) Post neoadjuvant chemotherapy, patients must be found to have residual invasive cancer in the breast at the time of definitive surgery; residual cancer is defined as a contiguous focus of residual invasive cancer, in the breast, measuring >= 1 cm in diameter, and with more than minimal cellularity, as per local pathologist determination; please note that in patients that have multifocal or multicentric residual tumors these lesions cannot be added up; the biggest lesion has to measure >= 1 cm in diameter; this is required due to constraints in deoxyribonucleic acid (DNA) extraction for PAM50 analysis\r\n* NOTE: The presence of ductal carcinoma in situ (DCIS) without invasion does not qualify as residual invasive disease in the breast\r\n* NOTE: Despite lymph node involvement if residual invasive cancer in the breast is < 1 cm in diameter patients are not eligible for participation No history of TNBC invasive breast cancer within 5 years of enrollment, no concurrent malignancies of any sort All patients must be diagnosed with invasive breast cancer Histologically confirmed invasive lobular breast cancer, that is hormone receptor-positive and HER2-negative, measuring at least 1 centimeter (cm) radiographically or clinically, clinical stages I-III; invasive lobular histology will be diagnosed at the enrolling institution for purposes of study participation; subsequently, invasive lobular histology will be confirmed by central pathology review, but this central review will not be required prior to patient enrollment Prior chemotherapy or radiation therapy for invasive breast cancer within 6 months before registration Prior investigational drugs or interventions for invasive breast cancer treatment within 6 months before registration are not allowed; prior participation in window-of-opportunity trials without therapeutic intent is allowed if intervention is no more than 3 weeks in duration Prior history of invasive breast cancer Have had or are planning to have the following invasive procedures: Histologic or clinical evidence of invasive breast cancer Patients with any active invasive cancer are not eligible No prior systemic therapy or radiotherapy for currently-diagnosed invasive or noninvasive breast cancer Prior systemic therapy for invasive or non-invasive (DCIS) breast cancer Bilateral invasive breast cancer Has invasive breast cancer; this does not include microinvasion No prior history of an invasive breast cancer Synchronous bilateral invasive or non-invasive breast cancer Scheduled to undergo non-nipple sparing mastectomy for Invasive Breast Cancer or DCIS within 1 month Any suspicion for invasive cancer Second invasive melanoma Synchronous bilateral invasive or non-invasive breast cancer Have had or are planning to have the following invasive procedures: Biopsy confirmed multifocal, multicentric, or contralateral disease that is invasive or non-invasive Histologic or cytologic confirmation of invasive breast cancer that is HER2-negative by standard clinical criteria Patients with core breast biopsy that, on pathology review, demonstrates invasive breast cancer and are determined to need surgical excision of the lesion; all subtypes of invasive breast cancer will be enrolled; core biopsy specimens of enrolled patients will be stained for RET by immunohistochemistry and scored, however, patients will not be excluded according to RET expression Prior history of DCIS or invasive breast cancer Synchronous bilateral invasive or non-invasive breast cancer Synchronous bilateral invasive breast cancer Known invasive breast cancer of any type Patients with multifocal, multicentric and synchronous bilateral breast cancers are allowed\r\n* Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant; (NOTE: the Oncotype DX testing must be completed on the largest lesion)\r\n* Multicentric disease is defined as more than one invasive cancer >= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants (NOTE: Oncotype DX testing should be completed on all tumors and the determination for eligibility should be made on the highest recurrence score)\r\n* Synchronous bilateral disease is defined as invasive breast cancer with positive lymph nodes (axillary or intramammary) in at least one breast, diagnosed within 30 days of each other; (NOTE: the Oncotype DX testing should be completed on both tumors and the tumor with the highest recurrence score should be used) Note that patients with (i) non-invasive breast cancer (DCIS) alone, (ii) incidental (microscopic) nodal cancer without a primary tumor (pN1mi), or (iii) metastatic disease are excluded. No prior history of non-breast invasive malignancies in the past 1 year History of invasive breast cancer prior to the current diagnosis Patients with multifocal, multicentric and synchronous bilateral breast cancers are allowed:\r\n* Multifocal disease is defined as more than one invasive cancer < 2 cm from the largest lesion within the same breast quadrant\r\n* Multicentric disease is defined as more than one invasive cancer >= 2 cm from the largest lesion within the same breast quadrant or more than one lesion in different quadrants\r\n* Synchronous bilateral disease is defined as invasive breast cancer in both breasts, diagnosed within 30 days of each other Patients with a history of previous invasive breast cancer Any stage invasive breast cancer provided the primary breast tumor size is >= 1 cm History of another “active” invasive primary cancer requiring ongoing treatment The participant has confirmed HR+, HER2-, early stage resected invasive breast cancer without evidence of distant metastases. For patients with invasive breast cancer, pathologic N stage of N0, N0 (i-), or N0 (i+); pathologic staging of the axilla is not required for patients with pure DCIS History of prior invasive or in situ cancer in either breast Women with non-invasive disease or microinvasion are not eligible Participants must have a confirmed or suspected invasive or non-invasive bladder tumor (initial or recurrent) discovered on cystoscopy or radiologic imaging performed within 120 days of randomization Initial core biopsy showing invasive lobular cancer EGFR GERMLINE MUTATION TESTING: One of the following criteria:\r\n* Personal history of invasive lung cancer or one of the pre-invasive histologies associated with the development of lung cancer (adenocarcinoma in situ [AIS], minimally invasive adenocarcinomas [MIA] or atypical adenomatous hyperplasia [AAH]) and more than two affected family members with invasive lung cancer or one of the pre-invasive histologies associated with the development of lung cancer; OR\r\n* First-degree relatives of an individual enrolled in the study with a known EGFR germline mutation Any prior treatment for the current primary invasive breast cancer Bilateral invasive breast cancer Bilateral invasive breast cancer. Prior systemic therapy or radiotherapy for invasive or non-invasive breast cancer in the same breast as currently being treated. Any prior treatment for primary invasive breast cancer Bilateral invasive, multicentric, or metastatic breast cancer Use of minimally invasive surgery. History of invasive breast cancer Breast cancer for which patient is receiving endocrine therapy must have been histologically-proven stage I-III, endocrine-responsive (i.e., estrogen and/or progesterone receptor positive, according to local definition of positive, determined using immunohistochemistry [IHC]), and treated with curative intent\r\n* Note:\r\n** Patients with synchronous bilateral invasive breast cancer (diagnosed histologically within 2 months) are eligible\r\n** Patient with invasive breast cancer or synchronous bilateral invasive breast cancer (diagnosed histologically within 2 months) during pregnancy are eligible\r\n** Patients with breast cancer 1/2, early onset (BRCA1/2) mutations are eligible\r\n** Patients could have received neo/adjuvant chemotherapy, or other systemic therapy (e.g., neo/adjuvant human epidermal growth factor receptor 2 [HER2]-targeted therapy) according to institutional policy and patient’s desire Ever had a diagnosis of invasive or microinvasive breast cancer Diagnosis of any invasive gynecologic cancer without evidence of disease Elective minimally invasive operation The patient must have a diagnosis of an invasive or non-invasive breast cancer that was treated surgically by a partial mastectomy Surgical margins are negative for invasive or non-invasive breast cancer Diagnosed with operable invasive cancer No history of invasive cervical cancer Invasive breast cancer; areas of microinvasion or suspicious for microinvasion on the core biopsy is allowed No evidence of disease (in situ or invasive cancer that would normally be treated by resection) at trial entry as determined by the investigator; diagnosis of invasive cancer must be at least 5 years prior to initiation on trial Any current invasive cancer diagnosis Invasive cancer diagnosis within five years, excluding squamous or basal cell skin cancer; subjects with DCIS or stage I invasive cancer are eligible if they are at least 2 months from radiation or surgery and at least 1 year (yr) from chemotherapy or hormone therapy; RPFNA will be performed on the contralateral breast only in these instances Prior colon cancer (>= 3 years out from invasive cancer) Diagnosed with a first primary invasive ER+ breast cancer (stages I-IIIa) Prior excisional biopsy of the primary invasive breast cancer Subject has invasive lobular cancer Patients may be registered AFTER surgery and PRIOR TO radiation therapy if either of the criteria is met:\r\n* An area of atypia > 2 cm from the index lesion excised at the time of cancer operation is upgraded to DCIS or invasive carcinoma thereby identifying MIBC OR\r\n* Patient underwent resection of two or three foci of malignancy by breast conservation surgery with a minimum of one invasive focus of breast cancer and a minimum of 2 cm of normal breast tissue between the lesions on final pathology Prior or current LCIS, DCIS or invasive breast cancer in the opposite breast (i.e., bilateral disease is not allowed) No evidence of disease (in situ or invasive cancer that would normally be treated by resection) at trial entry as determined by the investigator Participants must have adequate accessible breast tissue as determined by the treating physician, consisting of one breast unaffected by invasive cancer, which has not been radiated; a history of prior pre-invasive breast cancer or benign biopsy of this breast will be permitted Post-menopausal woman with a diagnosis of invasive breast cancer (T1-3,pN0-2,M0) for which definitive surgery was performed during the previous 36 months. Pathological diagnosis of invasive adenocarcinoma of the breast Patients undergoing a partial mastectomy OR mastectomy for the treatment of an invasive or non-invasive breast malignancy Have been diagnosed with a HER2+ invasive cancer of the breast Patient has concurrent invasive bilateral breast malignancies or multicentric disease Patient is scheduled for brain surgery and/or another invasive procedure within the time period of one month prior to 18F-FSPG administration. Minimally invasive needle biopsies are allowed. Patients diagnosed with unilateral DCIS or invasive breast cancer Patients with invasive, inflammatory breast cancer or distant metastases will be excluded from participating in this study Patient must have a histologic diagnosis of invasive breast cancer Prior invasive breast cancer, prior mastectomy or breast radiation within 12 months Newly diagnosed primary breast cancer prior to initial definitive surgical treatment, including in situ and invasive cancer, stages 0 – III; pathologic confirmation of diagnosis is required PHASE II: Women with a history of breast cancer (invasive and non-invasive) and those diagnosed with Paget’s disease, inflammatory breast cancer or a phyllodes tumor Diagnosis of invasive breast cancer Diagnosed with invasive adenocarcinoma, or DCIS for which a SLNB is the recommended standard of care, or breast cancer with all of the following conditions met: Confirmed current or past diagnosis of invasive breast cancer