Annotation: This is the first volume of a three volume collection of Andrey Nikolaevich Tyurin’s Selected Works. It includes his most interesting articles in the field of classical algebraic geometry, written during his whole career from the 1960s; most of these papers treat different problems of the theory of vector bundles on curves and higher dimensional algebraic varieties. This theory is central to algebraic geometry and most of its applications. The spectrum of the problems considered is very broad, ranging from the geometry of stable vector bundles on algebraic curves to the description of symplectic structures and metrics on the moduli varieties of vector bundles on surfaces, from the method of superposition in the theory of mathematical instantons to the application of classical enumerative geometry to the description of differentiable structures on four manifolds, from the theory of theta functions and Lagrangian geometry to the construction of Delzant models in Quantum Conformal Field Theory.