This text has heavily strived to make calculus accessible to any one who is considering the subject. With the many applications of calculus in pure sciences and arts, this book presents the fundamental mathematical notions in a non-traditional way yet keeping to rigour of the proofs. No prior knowledge of calculus in needed for one to understand the concepts, they have all been drawn from scratch. The area and tangent problems have a deep connection via the fundamental theorem of calculus, the common denominator being limits. We have completely elaborated differential and integration techniques from first principles.