Gorbunov and Rubakov: Theory of the Early Universe, Hot Big Bang Theory
One of the main books for the course, includes most of the topics we touch upon. In some cases the derivations are not entirely transparent to the non-expert.
Weinberg: Cosmology
An excellent review of most modern topics in Cosmology by a leading particle physicist (not restricted to the particle physics aspects of Cosmology). Clear but occasionaly challenging.
Zee: Gravity in a Nutshell
Mostly an introductory GR book, but some of the Early Universe sections have lucid explanations of difficult concepts.
Bambi and Dolgov: Introduction to Particle Cosmology
Targeted to particle cosmology, it includes most of the topics that we cover and more.
Mike Guidry: Modern General Relativity. Black holes, Gravitational Waves and Cosmology
A recent introductory GR textbook which takes the student to various advanced topics. Mostly useful for the Cosmology section.
Carroll: Spacetime and Geometry
A classic GR introductory book with a chapter on the Universe expansion that reads fluently.