Birational geometry is a branch of mathematics that studies the relationships between algebraic varieties, which are geometric objects defined by polynomial equations. It focuses on understanding how these varieties can be transformed into one another through rational maps, which are functions that can be expressed as ratios of polynomials. This field often involves the concept of birational equivalence, where two varieties are considered equivalent if they can be transformed into each other by such maps, except on lower-dimensional subsets. Key tools in birational geometry include divisors, blow-ups, and minimal models, which help classify and analyze the properties of these varieties.