Esperanto was designed to be easy, and it delivers. Its regular grammar, phonetic spelling and transparent word-building mean motivated learners reach conversational ability in a fraction of the time a natural language demands. That makes it unusually well suited to book learning, though as with any language, real fluency comes from using it with people and texts.
One honest note: these books will build your grammar and reading quickly, but speaking and listening still need practice, whether through the language's active online communities, correspondence, or meetups. The books are the fast on-ramp, not the whole road.
Start speaking the basics
Begin with Teach Yourself Complete Esperanto, a full modern course that takes you from zero through solid working ability with dialogues and exercises. Then Being colloquial in Esperanto is the ideal follow-up, teaching how the language is actually used rather than just its rules, which is where many self-learners plateau. Esperanto: Learning and Using the International Language gives another well-structured pass to reinforce the foundations.
Nail the grammar
Because Esperanto's grammar is small and regular, one good reference locks it in. A Complete Grammar of Esperanto is the classic thorough treatment, and thanks to the language's design you can genuinely learn nearly all of it. This is the point where Esperanto's promise pays off: there are few exceptions to memorize, so time spent here goes a long way.
Read and connect
Now apply it. Gerda Malaperis! is a beloved graded reader, a short mystery written specifically to grow with a beginner's vocabulary. Mazi en Gondolando offers gentle story-based immersion, and Esperanto in the Modern World steps back to the culture, history and living community around the language, which is much of its appeal. Finish with La Fundamento de Esperanto, Zamenhof's founding document, the fixed base of the whole language and a fascinating text once you can read it.
Follow the full path in order, then take your Esperanto into its worldwide community to make it truly stick.