This book consists of 33 essays trying to show to a nonmathematical community what mathematics and its applications really are, why they are so important and how they influence our day to day life. The essays may be read independently. Thanks to a long experience with mathematics as a researcher and teacher, the author provides many creative discussions and examples, varying from simple to more abstract structures of mathematics. He tries to provide a leitmotif to illustrate the relationship between mathematics and common sense. He writes about more than sixty major topics in mathematics, many of which have significant connections to other branches of knowledge (e.g. cosmology, physics, teaching, logic, philosophy, languages). The reader can find discussions on the nature of logic, numbers, counting and discounting, mathematical thinking, deductions, intuition and creativity, problem solving, conceptions of space, mathematical operations, structures, objects, paradoxes, theorems and proofs, as well as meditations on the influence of the media and wars on the development of mathematics and its position in the society. The author states and answers many interesting questions from many points of view. At the end of each essay the references to material that is both popular and professional are given. The book can be recommended to all who are interested in mathematics and its nature, beauty and role in modern society and science.