The mathematical model designing is an important part in the evolution of present computer systems. The abstract machine is based on the mathematical model designing. The basic abstract machine is Finite Automata. The other two abstract machines are Pushdown Automata and the Turing Machine. This book mainly focuses on problems along with the solutions in Finite Automata. Totally 50 questions are given. The questions are based on simple mathematical concepts. There may be two similar problems. But the solution may be slightly different and its variations will be known to the readers.