Einstein's connection in a generalized Riemannian manifold X n has been investigated by many authors for lower-dimensional cases n = 2 , … , 6 . In a series of papers, we obtain a surveyable tensorial representation of 7 -dimensional Einstein's connection in terms of unified field tensor, with main emphasis on the derivation of powerful and useful recurrence relations which hold in X 7 . In this paper, we give a brief survey of Einstein's unified field theory and derive the recurrence relations of the first kind which hold in a general X n . All considerations in this paper are restricted to the first and second classes only since the case of the third class, the simplest case, was already studied by many authors.