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This is an introduction to background independent quantum theories of gravity, with a focus on loop quantum gravity and related approaches. Basic texts: -Quantum Gravity, by Carlo Rovelli, Cambridge University Press 2005 -Quantum gravityy with a positive cosmological constant, Lee Smolin, hep-th/0209079 -Invitation to loop quantum gravity, Lee Smolin, hep-th/0408048 -Gauge fields, knots and gravity, JC Baez, JP Muniain Prerequisites: -undergraduate quantum mechanics -basics of classical gauge field theories -basic general relativity -hamiltonian and lagrangian mechanics -basics of lie algebras

The TeV energy range is a privileged part of the EM spectrum for astrophysical observations, allowing a view of some of the most energetic processes in the Universe, in objects as diverse as supernova remnants and black-hole driven Active Galactic Nuclei. Driven by new instruments, TeV gamma-rays astrophysics has made enormous strides in recent years with the discovery of many new sources, including new classes of sources such as galactic micro-quasars. This talk will give an overview of the state of TeV gamma-ray astrophysics, including the air Cherenkov technique used by ground-based TeV gamma ray detectors, the new instruments in operation or coming on line soon, and some of the results already obtained.

We will postulate a novel notion of probability; this will involve introducing an extra axiom of probability that seems natural from a Bayesian perspective. We will then provide an analogue of Gleason's theorem for these probabilities. We will also discuss why this approach may be useful for generalizations of quantum theory such as quantum gravity theories; this will involve discussing an analogy between Bayesian approaches and relational approaches.