This book is mostly based on the author's 25 years of teaching combinatorics to two distinct sets of students first-year students and seniors from all backgrounds, not just limited to only those majoring in mathematics and physics. The prerequisites are kept to a minimum essentially, only high school algebra is required. The design is to go from zero knowledge to advanced themes and various applications during a semester of three or three and a half months with quite a few topics intended for research projects and additional reading.This unique book features the key themes of classical introductory combinatorics, modeling mainly linear, and elementary number theory with a constant focus on applications in statistics, physics, biology, economics, and computer science. These applications include dimers, random walks, binomial and Poisson distributions, games of chance lottery, dice, poker, roulette, pricing options, population growth, tree growth, modeling epidemic spread, invasion ecolo