This book is based on the author's mini course delivered at Tokyo University of Marine Science and Technology in March 2019. brThe shuffle approach to Drinfeld-Jimbo quantum groups of finite type embedding their positive subalgebras into q-deformed shuffle algebras was first developed independently in the 1990s by J. Green, M. Rosso, and P. Schauenburg. Motivated by similar ideas, B. Feigin and A. Odesskii proposed a shuffle approach to elliptic quantum groups around the same time. The shuffle algebras in the present book can be viewed as trigonometric degenerations of the Feigin-Odesskii elliptic shuffle algebras. They provide combinatorial models for the positive subalgebras of quantum affine algebras in their loop realizations. These algebras appeared first in that context in the work of B. Enriquez.brOver the last decade, the shuffle approach has been applied to various problems in combinatorics combinatorics of Macdonald polynomials and Dyck paths, generalization to wreath Macdona