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The last decade has seen an explosive increase in both the volume and the accuracy of data obtained from cosmological observations. The number of techniques available to probe and cross-check these data has similarly proliferated in recent years.

Theoretical cosmologists have not been slouches during this time, either. However, it is fair to say that we have not made comparable progress in connecting the wonderful ideas we have to explain the early universe to concrete fundamental physics models. One of our hopes in these lectures is to encourage the dialogue between cosmology, particle physics, and string theory that will be needed to develop such a connection.

In this paper, we have combined material from two sets of TASI lectures (given by SMC in 2002 and MT in 2003). We have taken the opportunity to add more detail than was originally presented, as well as to include some topics that were originally excluded for reasons of time. Our intent is to provide a concise introduction to the basics of modern cosmology as given by the standard "LambdaCDM" Big-Bang model, as well as an overview of topics of current research interest.

In Lecture 1 we present the fundamentals of the standard cosmology, introducing evidence for homogeneity and isotropy and the Friedmann-Robertson-Walker models that these make possible. In Lecture 2 we consider the actual state of our current universe, which leads naturally to a discussion of its most surprising and problematic feature: the existence of dark energy. In Lecture 3 we consider the implications of the cosmological solutions obtained in Lecture 1 for early times in the universe. In particular, we discuss thermodynamics in the expanding universe, finite-temperature phase transitions, and baryogenesis. Finally, Lecture 4 contains a discussion of the problems of the standard cosmology and an introduction to our best-formulated approach to solving them - the inflationary universe.

Our review is necessarily superficial, given the large number of topics relevant to modern cosmology. More detail can be found in several excellent textbooks [1, 2, 3, 4, 5, 6, 7]. Throughout the lectures we have borrowed liberally (and sometimes verbatim) from earlier reviews of our own [8, 9, 10, 11, 12, 13, 14, 15].

Our metric signature is - + + +. We use units in which hbar = c = 1, and define the reduced Planck mass by MP ident (8pi G)-1/2 appeq 1018 GeV.

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