Some content moved to Simplicial techiques
Dundas is also a good reference. See also Pointed simplicial set
Def of Kan fibration and other useful things at nLab
nLab also here and simplicial homotopy groups
Model structures from nLab
Simplicial group from nLab
arXiv:0809.4221 An elementary illustrated introduction to simplicial sets from arXiv Front: math.CT by Greg Friedman This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to students familiar with just the fundamentals of algebraic topology.
nLab page on Simplicial set