Mendelian genetics is the study of how traits are inherited from one generation to the next, based on the work of Gregor Mendel, an Austrian monk. He conducted experiments with pea plants and discovered that traits are passed down through discrete units called genes. These genes can be dominant or recessive, influencing the appearance of specific characteristics. Mendel's principles include the Law of Segregation, which states that each parent contributes one allele for each trait, and the Law of Independent Assortment, which explains how different traits are inherited independently. These foundational concepts help us understand the genetic basis of inheritance in all living organisms.