Equivariant cohomology in algebraic geometry Equivariant cohomology has become an indispensable tool in algebraic geometry and in related areas including representation theory combinatorial and enumerative geometry and algebraic combinatorics. This text introduces the main ideas of the subject for first or second year graduate students in mathematics as well as researchers working in algebraic geometry or combinatorics. The first six chapters cover the basics: definitions via finite dimensional approximation spaces computations in projective space and the localization theorem. The rest of the text focuses on examples – toric varieties Grassmannians and homogeneous spaces – along with applications to Schubert calculus and degeneracy loci. Prerequisites are kept to a minimum so that one semester graduate level courses in algebraic geometry and topology should be sufficient preparation. Featuring numerous exercises examples and material that has not previously appeared in textbook form this book will be a must have reference and resource for both students and researchers for years to come.