A fellowship is taken after a residency that allows the physician/surgeon to concentrate their practice in a specific area of their residency. For example:
Residency: Internal medicine
Fellowship: Gastroenterology, cardiology, rheumatology, nephrology, etc, etc, etc...
Residency: General surgery
Fellowship: Cardiothoracic surgery, transplant surgery, vascular surgery, colorectal surgery, etc, etc, etc...
Residency: Pathology
Fellowship: Neuopathology, dermpathology, etc.
Residency: Family medicine
Fellowship: Geriatric medicine, sports medicine.
The list is quite extensive.
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