An Introduction to Manifolds

An Introduction to Manifolds is a mathematics textbook written by Loring W. Tu providing an introduction to differential and integral calculus on smooth manifolds. It was first published in 2008 by Springer and received positive reviews. The book is meant as a precursor to Differential Forms in Algebraic Topology by Raoul Bott and Tu.

References

↑ Tu, Loring W. (2011). An Introduction to Manifolds. Universitext. Springer. doi:10.1007/978-1-4419-7400-6. ISBN 978-1-4419-7399-3.
↑ Berg, Michael (April 19, 2008). "An Introduction to Manifolds". MAA Reviews. Mathematical Association of America. Retrieved 2025-09-19.
↑ Cap, A. (September 25, 2010). "Book Reviews". Monatshefte für Mathematik. 161 (3). SpringerLink: 354. doi:10.1007/s00605-010-0237-5.
↑ Feldman, D. V. (June 2008). "An Introduction to Manifolds". Choice: Current Reviews for Academic Libraries. 45 (10): 1807. doi:10.5860/CHOICE.45-5637 (inactive 19 September 2025). ProQuest 225728177.{{cite journal}}: CS1 maint: DOI inactive as of September 2025 (link)
↑ Bott, Raoul; Tu, Loring W. (1982). Differential Forms in Algebraic Topology. Graduate Texts in Mathematics. Vol. 82. Springer. doi:10.1007/978-1-4757-3951-0. ISBN 978-1-4419-2815-3.

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[1] Tu, Loring W. (2011). An Introduction to Manifolds. Universitext. Springer. doi:10.1007/978-1-4419-7400-6. ISBN 978-1-4419-7399-3.

[2] Berg, Michael (April 19, 2008). "An Introduction to Manifolds". MAA Reviews. Mathematical Association of America. Retrieved 2025-09-19.

[3] Cap, A. (September 25, 2010). "Book Reviews". Monatshefte für Mathematik. 161 (3). SpringerLink: 354. doi:10.1007/s00605-010-0237-5.

[4] Feldman, D. V. (June 2008). "An Introduction to Manifolds". Choice: Current Reviews for Academic Libraries. 45 (10): 1807. doi:10.5860/CHOICE.45-5637 (inactive 19 September 2025). ProQuest 225728177.{{cite journal}}: CS1 maint: DOI inactive as of September 2025 (link)

[5] Bott, Raoul; Tu, Loring W. (1982). Differential Forms in Algebraic Topology. Graduate Texts in Mathematics. Vol. 82. Springer. doi:10.1007/978-1-4757-3951-0. ISBN 978-1-4419-2815-3.