An Invitation to Knot Theory: Virtual and Classical gives you a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for you to research knot theory and read journal articles on your own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation. Features: Covers virtual knots and other versions of knot equivalence -- the only knot theory textbook to do so - Describes how proof strategies are used - Incorporates many examples gathered directly from current research as well as well-known applications and results for classical knots and links - Includes problem sets and suggestions for undergraduate projects in each chapter - Provides further reading recommendations based on peer-reviewed journals. --