This book covers the material found in most first undergraduate courses in Real Analysis. Where it is different is that instead of teaching limits first, then defining continuity, differentiability and integrability by means of limits, this book defines continuity first, using a geometrical-based definition, then uses that to define differentiability and integrability. Limits are introduced later, together with sequences and series where they occur more naturally. It is claimed that this provides a conceptually easier appraoch to a student's first meeting with Real Analysis.