Eventually I’ll add some more detailed descriptions here. For now: the most accessible of these books is probably either McLarty or Goldblatt. The Elephant is comprehensive and correspondingly hard work.
- Peter Johnstone (2002): Sketches of an Elephant
- Colin McLarty (2005): Elementary Categories, Elementary Toposes
- Robert Goldblatt (1984): Topoi: The Categorial Analysis of Logic
- Peter Johnstone (1977): Topos Theory
- Saunders Mac Lane and Ieke Moerdijk (1992): Sheaves in Geometry and Logic: A First Introduction to Topos Theory
- Olivia Caramello (2018): Theories, Sites, Toposes
- John L. Bell (1988): Toposes and Local Set Theories: An Introduction