references to learn the general theory Lie $\infty$-groupoids and Lie $\infty$-algebroids

Question

Kirill Mackenzie has a book on the general theory of Lie groupoids and Lie algebroids.

Is there such a reference for the general theory of Lie $\infty$-groupoids and Lie $\infty$-algebroids; that covers some of the following topics:

1. Definition(s) and examples of Lie $\infty$-groupoids, Lie $\infty$-algebroids.
2. Some constructions of new Lie $\infty$-groupoids from old Lie $\infty$-groupoids; similarly for Lie $\infty$-algebroids
3. assigning Lie $\infty$-algebroid for a Lie $\infty$-groupoid
4. some details about ''integration of Lie $\infty$-algebroid'' to give a Lie $\infty$-groupoids.

Or, as a first step, reference for the general theory of Lie $2$-groupoids and Lie $2$-algebroids.

Answer 1

There is no introductory book on Lie ∞-groupoids and ∞-algebroids analogous to Mackenzie's book. The only book-length treatment that covers these subjects is Urs Schreiber's Differential cohomology in a cohesive ∞-topos.

Otherwise, the material is scattered over many sources.

Some annotated lists of references can be found on the nLab: 1, 2, 3.

Čech cocycles for differential characteristic classes – An ∞-Lie theoretic construction is one of the more accessible introductory articles, though it requires some knowledge of modern homotopy theory.