This Gedenkschrift for Peter Carr, our dear friend and colleague who suddenly left us on March 1, 2022, was organized to honor the life and lasting contributions of Peter to Quantitative Finance. A group of Peter's co-authors and professional friends contributed chapters for this Gedenkschrift shortly after his passing. The papers were received by September 15, 2022 and some were presented at the Peter Carr Gedenkschrift Conference held at the Robert H Smith School of Business on November 11, 2022. The contributed papers cover a wide range of topics corresponding to the vast range of Peter's interests. Each paper represents new research results in recognition of Peter's scholarly activities. The book serves as an important marker for the research knowledge existing at the time of the Gedenkschrift's publication on a number of topics within quantitative finance. It reflects the diverse interactions between mathematics and finance and illustrates, for those interested, the breadth and depth of this development. The book also presents a collection of tributes to Peter from family and friends including those made at his Memorial Service on March 19, 2022. The result is hopefully a more complete testament to a personal and professional life well lived, and unexpectedly cut short.