Reference for Gauss-Manin connection I wish to understand the notion of ``Gass-Manin connection''. I have some understanding of differential geometry, topology and algebraic geometry. Where should I begin? IF the sources are freely available, that will be good. Even better will be if someone can give some little motivation for the concept. My aim is to understand it in the context of moduli of curves.

Let $π : X \to T$ be a smooth algebraic family of complex projective manifolds of
dimension d such that the parameter space $T$ is a nonsingular variety. Consider the local
systems $R^kπ_∗\mathbb C$, $0 ≤ k ≤ 2d$, and the associated vector bundles 
$\mathcal H^k:= (R^kπ_∗\mathbb C)\otimes_\mathbb C \mathcal O_T$
over $T$. These vector bundles are equipped with the Gauss–Manin connection. 
See this Master thesis written in French 
