These proceedings summarize lectures that were delivered as part of the 2002 and 2003 Theoretical Advanced Study Institutes in elementary particle physics (TASI) at the University of Colorado at Boulder. They are intended to provide a pedagogical introduction to cosmology aimed at advanced graduate students in particle physics and string theory.

It is well-expected that unifying gravity with other interactions requires a decisive change of perspective on some of our ideas. We can mention String Theory as the most suggestive approach in this direction. Here we are going to focus our attention on the Kaluza-Klein (KK) approach 1,2 (see 3 for a recent review), since it realizes the issue of the unification, without avoiding one of the mos...

In theoretical physics, paradoxes are good. That’s paradoxical, since a paradox appears to be a contradiction, and contradictions imply serious error. But Nature cannot realize contradictions. When our physical theories lead to paradox we must find a way out. Paradoxes focus our attention, and we think harder. When David Gross and I began the work that led to this Nobel Prize [1, 2, 3, 4], in 1...

We present a broad review on black holes. We analyse some of the fundamental concepts in black hole theory, the observational and theoretical status of stellar and galactic black holes, and their appearance

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An introduction to the minimal supersymmetric Standard Model (MSSM) is given. The motivation for “low-energy” supersymmetry is reviewed, and the structure of the MSSM is outlined. In its most general form, the MSSM can be viewed as a low-energy effective theory parametrized by a set of arbitrary soft-supersymmetry-breaking parameters. A variety of techniques for reducing the parameter freedom o...

It is shown, that our contemporary knowledge of geometry is insufficient, because we know only axiomatizable geometries. With such a knowledge of geometry one cannot investigate properly physics of microcosm and structure of elementary particles. One can obtain only a phenomenological systematics of elementary particles, whose construction does not need a discrimination mechanism. The discrimin...