Introduction to the video and the approach to learning mathematics from the basics to advanced levels.

• The presenter outlines the intent to show how to learn mathematics from start to finish, beginning with the basics.
• Three different ways to get started with mathematics are presented, with the option to pursue all three simultaneously.
• The goal is to offer starting points for learning mathematics that cater to different preferences or learning styles.

Starting the mathematics learning journey with algebra using various recommended textbooks.

• Algebra is introduced as a common starting point for learning math, with pre-algebra and elementary algebra books suggested.
• Nickels' 'Pre-Algebra Mathematics' is recommended for learning the very basics of algebra.
• For a slightly more advanced start, 'Elementary Algebra' by Sullivan, Struve, and Mazzarella is suggested, complete with examples and essential algebra concepts.

An unconventional approach to beginning math learning through discrete mathematics with book recommendations.

• Discrete math is presented as an unconventional starting point, typically approached after calculus 2 in the United States.
• Books such as 'Discrete Mathematical Structures' by Coleman, Busby, and Ross offer a beginner-friendly introduction to the subject.
• The presenter highlights the importance of learning logic and mathematical proofs for advancing beyond calculus.

Introducing proof writing as an exciting way to get started with mathematics, with multiple book suggestions.

• Proof writing is suggested as a fun and rewarding way to begin learning mathematics.
• Books such as 'How to Prove It' by Daniel Velleman and 'An Introduction to Abstract Mathematics' by Bond and Keane are recommended.
• The presenter shares personal experiences with some of the books and emphasizes the importance of understanding logic in mathematics.

Guidance on moving from basic algebra and trigonometry to calculus and higher mathematics with specific book recommendations.

• After mastering basic algebra and trigonometry, one is prepared to move onto calculus.
• The video suggests taking courses like pre-calculus and trigonometry to build a foundation for calculus.
• Books like 'College Algebra' by Blitzer and 'Precalculus Mathematics' by Shanks, Fleener, and Eichholz are introduced as resources to prepare for calculus.

Exploration of higher-level mathematics topics including differential equations, probability, statistics, and geometry.

• After learning calculus, the next steps include differential equations, probability, statistics, and geometry.
• Differential equations books by Nagle, Saff, and Snyder, as well as by Dennis Zill, are recommended for further study.
• For probability and statistics, books like 'Elementary Statistics' by Weiss and 'Mathematical Statistics and Data Analysis' by John Rice are suggested.

Recommendations for studying linear algebra and complex variables with a variety of textbooks suitable for different levels.

• Linear algebra is introduced with beginner-friendly books like 'Elementary Linear Algebra' by Howard Anton.
• For complex variables, 'Complex Variables and Applications' by Brown and Churchill is presented as a standard introductory textbook.
• The presenter also includes a selection of more advanced books for both subjects, like 'Algebra' by Michael Artin for linear algebra.

Guidance on approaching partial differential equations and abstract algebra with specific book suggestions for each topic.

• The study of partial differential equations is suggested after mastering ordinary differential equations, with books like 'Partial Differential Equations' by Zachmanoglou recommended.
• For abstract algebra, 'A First Course in Abstract Algebra' by John B. Fraleigh and 'Algebra' by Michael Artin are presented for different experience levels.

Introduction to advanced calculus or real analysis with book recommendations for different learning stages.

• For those ready for advanced calculus or real analysis, the video suggests 'Advanced Calculus' by Fitzpatrick and 'Understanding Analysis' by Abbott.
• The presenter shares personal experiences and preferences for textbooks, noting 'Advanced Calculus' by Buck as a favorite.

An assortment of books on various mathematics topics, from number theory to topology, functional analysis, and beyond.

• Books covering number theory, graph theory, and topology are presented, with recommendations based on the presenter's experiences.
• Functional analysis and cryptography are introduced with suitable textbooks for those interested in specialized mathematics fields.
• The video concludes with a diverse selection of mathematics books that can enhance any mathematical education journey.