This book presents a collection of invited articles by distinguished Mathematicians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute, during the year 2007. These articles provide a current perspective of different areas of research, emphasizing the major challenging issues. Given the very significant record of the Institute in research in the areas of Statistics, Probability and Mathematics, distinguished authors have very admirably responded to the invitation. Some of the articles are written keeping students and potential new entrants to an area of mathematics in mind. This volume is thus very unique and gives a perspective of several important aspects of mathematics. Use of Resultants and Approximate Roots for Doing the Jacobian Problem (S S Abhyankar) Monodromy of Principal Bundles (I Biswas & A J Parameswaran) Oligomorphic Permutation Groups (P J Cameron) Descriptive Set Theory and the Geometry of Banach Spaces (G Godefroy) Multiplicity-Free Homogeneous Operators in the Cowen Douglas Class (A Kor??nyi & G Misra) The Standard Conjectures on Algebraic Cycles (M S Narasimhan) On the Classification of Binary Shifts on the Hyperfinite II1 Factor (G L Price) Symmetric and Quasi-Symmetric Designs and Strongly Regular Graphs (S S Sane) Perturbation Determinant, Krein's Shift Function and Index Theorem (K B Sinha) Zero Cycles and Complete Intersection Points on Affine Varieties (V Srinivas) Root Numbers and Rational Points on Elliptic Curves (R Sujatha) von Neumann Algebras and Ergodic Theory (V S Sunder) Gutzmer's Formula and the Segal Bargmann Transform (S Thangavelu) Finite Translation Generalized Quadrangles (J A Thas) Super Geometry as the Basis for Super Symmetry (V S Varadarajan)