These lectures present a brief review of inflationary cosmology, provide an overview of the theory of cosmological perturbations, and then focus on the conceptual problems of the current paradigm of early universe cosmology, thus motivating an exploration of the potential of string theory to provide a new paradigm. Specifically, the string gas cosmology model is introduced, and a resulting mechanism for structure formation which does not require a period of cosmological inflation is discussed.

Invited lectures at the Summer School on Particle Physics, Gravity and Cosmology (Dubrovnik, August 2006), publ. in the on-line proceedings (PoS(P2GC)007). 46 pages, 5 figures