Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields.Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.1. General concepts; 2. Internal structure of categories; 3. Homological algebra; 4. Sheaves and their cohomology.