This is an introductory textbook on general and algebraic topology aimed at anyone with a
basic knowledge of calculus and linear algebra. It provides full proofs and includes many
examples and exercises. The covered topics include: set theory and cardinal arithmetic axiom
of choice and Zorn's lemma topological spaces and continuous functions connectedness and
compactness Alexandrov compactification quotient topologies countability and separation
axioms prebasis and Alexander's theorem the Tychonoff theorem and paracompactness complete
metric spaces and function spaces Baire spaces homotopy of maps the fundamental group the
van Kampen theorem covering spaces Brouwer and Borsuk's theorems free groups and free
product of groups and basic category theory. While it is very concrete at the beginning
abstract concepts are gradually introduced. It is suitable for anyone needing a basic
comprehensive introduction to general and algebraic topology and its applications.
