The proposed research program intends to cover all aspects of the problem of learning and analyzing collections of surfaces and apply the developed methods and algorithms to a wide range of scientific data.The proposal has two parts:In the first part of the proposal, we concentrate on developing the most basic operators comparing automatically pairs of surfaces. Although this problem has receiveda lot of attention in recent years,and significant progress has been made, there is still a great need for algorithms that are both efficient/tractable and come with guaranteesof convergence or accuracy. The main difficulty in most approaches so faris that they work in a huge and non-linear search space to compare surfaces; most algorithms resort to gradient descent from an initial guess, risking to find only local optimal solution.We offer a few research directions to tackle this problem based on the idea of identifying EFFICIENT search spaces that APPROXIMATE the desired optimal correspondence.In the second part of the proposal we propose to make use of the methods developed in the first part to perform global analysis of, or learn, collections of surfaces. Weput special emphasis on ``real-world'' applications and intend to validate our algorithm on a significant collection, including data-sets such as biological anatomic data-sets and computer graphics' benchmark collections of surfaces. We propose to formulate and construct geometric structures on these collections and investigate their domain specific implications.