This course is an introduction to the theory of universal mixed elliptic motives, much of which I have developed with Makoto Matsumoto.
Lecture Notes and Vidoes:
Specific References:
These are expository papers I have written.
This is a reasonably complete elementary description of the moduli space of elliptic curves as an orbifold.
This is an exposition of Chen's iterated integrals, their relation to unipotent completion, and an introduction to the MHS on unipotent fundamental groups of a smooth variety.
This paper gives a detailed description of the construction of the MHS on the coordinate ring of the relative completion of the modular group SL_{2}(Z). It also contains a discussion of extensions of certain variations of MHS over the modular curve.
The first part of this paper is an exposition of the work of Calaque-Enriquez-Etingof [arXiv:math/0702670] and Levin-Racinet [arXiv:math/0703237] on what amounts to the Q-de Rham theory of the local system of unipotent fundamental groups of punctured elliptic curves over the universal elliptic curve.
This paper contains an exposition of relative weight filtrations written for topologists. Although the focus is generally on moduli of curves genus larger than 1, the exposition is still relevant in the elliptic case.
General References:
Here are several useful references on elliptic curves. The first and third books contain useful information about elliptic curves that can be used to give a description of the moduli stack of elliptic curves over Z. The second book has an exposition of the Tate curve. The fourth is the basic (and an excellent) reference for mixed Hodge structures and their construction.
Additional References:
Notes:
These are extacts from a manuscript Universal Mixed Elliptic Motives being written with Makoto Matsumoto.
You can find the bibliographic references here (pdf).