  This is the first in a series of articles where we will study the Iwasawa
theory of an elliptic modular form f along the anticyclotomic Zp-tower of an
imaginary quadratic field K where the prime p splits completely. Our goal in
this portion is to prove the Iwasawa main conjecture for suitable twists of f
assuming that f is p-ordinary, both in the definite and indefinite setups
simultaneously, via an analysis of Beilinson-Flach elements.
