There are several excellent references on the physics of the early universe. The primary focus of this course will be the particle physics of the (homogeneous) early universe. The recommended course textbook is a relatively new book by Baumann. This excellent textbook is based on Baumann's publicly available lecture notes. We will mostly be using the first half of this textbook in class, covering the homogeneous early universe. In the second half of the course we will also use lecture notes and review articles in our discussion of various particle physics topics. Specific readings will be posted to the course schedule page.
Beyond Baumann, Kolb and Turner is the classic reference on this topic. There have been many advances in our experimental understanding of the early universe since its first publication, but nonetheless it remains an excellent general reference and introduction to the field.