Here are some references on Quillen model categories:

  • Daniel Quillen (1967): Homotopical Algebra. Springer-Verlag, ISBN 978-0-387-03914-5
  • Mark Hovey (1999): Model categories. AMS, ISBN 978-0-8218-1359-1
  • Philip Hirschhorn (2003): Model Categories and Their Localizations. AMS, ISBN-10: 0-8218-4917-4, ISBN-13: 978-0-8218-4917-0,
  • Peter May and Kate Ponto (2012): More Concise Algebraic Topology, Chapters 14-19. Chicago, ISBN-10: 0226511782, ISBN-13:978-0226511788
  • Dwyer and Spalinski, Homotopy theory and model categories, Handbook of Algebraic Topology, 1995.
    Available here:

On the web:

Here is Peter Lumsdaine's paper on a (pre-)Quillem model structure in type theory: