This book covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. It features a self-contained presentation of the cone pseudo-differential calculus; a general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and a new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.