The delicate connective tissue that surrounds the skeletal muscle fibers and ties adjacent muscle fibers together is the

Endomysium

Explanation:

Endomysium is a thin layer of loose connective tissue which surrounds an individual myocyte or muscle fiber. Collagen is one of the most abundant protein found in this layer. Endomysium also connects the near by muscle fibers to each other. These fibers are then able to exchange various ions necessary for muscle contraction.

Above the level of endomysium, there is perimysium which forms the covering of a bundle of muscle fibers. Even above this level is epimysium which covers the whole muscle.