This book focuses on some important classical parts of Geometry, Analysis and Number theory. The material is divided into ten chapters, including new advances on triangle or tetrahedral inequalities; special sequences and series of real numbers; various algebraic or analytic inequalities with applications; special functions(as Euler gamma and beta functions) and special means( as the logarithmic, identric, or Seiffert's mean); Arithmetic functions and arithmetic inequalities with connections to perfect numbers or related fields; and many more. The majority of the presented topics are based on the original journal publications of the author. This reference work will be useful for undergraduate university or college students; as well as teachers, researchers and professors interested in these fields of mathematics.