The whole book is presented as a relatively free-flowingdialogue between the AUTHOR and the READER. From one discussionto another the AUTHOR will lead the inquisitive and receptiveREADER to different notions, ideas, and theorems of calculus,emphasizing especially complicated or delicate aspects, stressing theinner logic of proofs, and attracting the reader's attention to specialpoints. I hope that this form of presentation will help a reader of thebook in learning new definitions such as those of derivative, antiderivative, definite. integral, differential equation, etc. I also expect thatit will lead the reader to better understanding of such concepts asnumerical sequence, limit of sequence, and function. Briefly, thesediscussions are intended to assist pupils entering a novel world ofcalculus. And if in the long run the reader of the book gets a feelingof the intrinsic beauty and integrity of higher mathematics or evenis appealed to it, the author will consider his mission as successfullycompleted.