This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous year or so. Mathematics is constantly growing and changing, reaching out to other areas of science and helping to solve some of the major problems facing society. Volumes 1 and 2 survey some of the important developments in the mathematical sciences over the past year or so. The contents of volume 1 are: (1) "Equations Come to Life in Mathematical Biology"; (2) "New Computer Insights from 'Transparent' Proofs"; (3) "You Can't Always Hear the Shape of a Drum"; (4) "Environmentally Sound Mathematics"; (5) "Disproving the Obvious in Higher Dimensions"; (6) "Collaboration Closes in on Closed Geodesics"; (7)"Crystal Clear Computations"; (8) "Camp Geometry"; (9) "Number Theorists Uncover a Slew of Prime Impostors"; and (10) "Map-Coloring Theorists Look at New Worlds." The contents of volume 2 are: (1) "A Truly Remarkable Proof" (Fermat's Last Theorem); (2) "From Knot to Unknot"; (3) "New Wave Mathematics"; (4) "Mathematical Insights for Medical Imaging"; (5) "Parlez-vous Wavelets?" (6) "Random Algorithms Leave Little to Chance"; (7) "Soap Solution"; (8) "Straightening Out Nonlinear Codes"; (9) "Quite Easily Done"; and (10) "(Vector) Field of Dreams." (MKR).