In this paper we will discuss the geometry of ﬁnite topology properly embedded minimal surfaces M in R3 . M of ﬁnite topology means M is homeomorphic to a compact surface M (of genus k and empty boundary) minus a ﬁnite number of points p1 , ., pj ∈ M , called the punctures. A closed neighborhood E of a puncture in M is called an end of M . We will choose the ends suﬃciently small so they are topologically S 1 × [0, 1) and hence, annular. We remark that M is orientable since M is properly.