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In this series of lectures, we will develop deformation theory of functors of Artin rings. After discussing extensions of algebras over a fixed base ring, we will develop the theory of functors of Artin rings. These occur as 'local' versions of various moduli problems, and can give information about the local structure (e.g. smoothness, dimension) of moduli spaces near a point. We apply the theory to concrete examples of moduli problems, such as invertible sheaves on a variety, Hilbert schemes and Quot schemes. Reference: Deformations of Algebraic Schemes, Edoardo Sernesi, Springer-Verlag, 2006. (Grundlehren der mathematischen Wissenschaften, no. 334)