Boundary value problems on manifolds with singularities In the thesis there are constructed new quantizations for pseudo differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case here with edge and boundary is much more complicated. The present approach simplifies the operator valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are modulo smoothing ones with asymptotics holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra including elliptic edge conditions.