Introduction to supergravity

These lectures present an introduction to supergravity, and are intended for graduate students with a working knowledge of quantum field theory, including the elementary group theory needed for it, but no prior knowledge of general relativity, supersymmetry or string theory is assumed. I will start by introducing the needed elements of general relativity and supersymmetry. I will then describe the simplest cases of supergravity, ${\cal N}=1$ on-shell in 4 dimensions and ${\cal N}=1$ off-shell in 3 dimensions. I will introduce superspace formalisms in their simplest cases, and apply them to ${\cal N}=1$ in 4 dimensions, after which I will show how to couple to matter using superspace. I will introduce the procedure of KK dimensional reduction and describe general supergravity theories, in particular the unique 11 dimensional supergravity. I will then exemplify the issues of KK dimensional reduction on the only complete example of full nonlinear compactification, on the gravitational space $AdS_7\times S^4$. Finally, I will show how we can use supergravity compactifications together with some string theory information, for realistic embeddings of the Standard Model, via ${\cal N}=1$ supergravity in 4 dimensions.