* 安德拉斯·I·斯蒂普西茨和罗伯特·E·贡普夫的《4-流形与柯比微积分》（4-Manifolds and Kirby Calculus）* 安东尼·A·科辛斯基的《微分流形》（Differential Manifolds）* 约翰·M·李的《光滑流形导论》（Introduction to Smooth Manifolds）
* 4-Manifolds and Kirby Calculus by Andras I. Stipsicz and Robert E. Gompf * Differential Manifolds by Antoni A. Kosinski * Introduction to Smooth Manifolds by John M. Lee
I first learned about manifolds through Introduction to Smooth Manifolds by John M. Lee. The book is dense but beautifully structured, guiding you from basic topology to smooth maps and tangent spaces with clear logic. It demands focus, yet every definition builds toward a…
…through Baby Rudin. For topology specifically you can look into Munkres or Introduction to Topological Manifolds, J Lee. > Measure Theory T. Tao has a good book on this topic. > Differential Geometry Introduction to Smooth Manifolds by J Lee > Probability Probability Theory, Achim Klenke > Game Theory Game Theory by Maschler, Solan & Zamir
That's a great suggestion. I actually started with Topological Manifolds before moving on to Introduction to Smooth Manifolds and it really helped build a solid foundation. I havent read Loring Tus books before but let me look at them since I have been wanting to revisit the topic with a clearer and more relaxed approach.
* 安德拉斯·I·斯蒂普西茨和罗伯特·E·贡普夫的《4-流形与柯比微积分》（4-Manifolds and Kirby Calculus）* 安东尼·A·科辛斯基的《微分流形》（Differential Manifolds）* 约翰·M·李的《光滑流形导论》（Introduction to Smooth Manifolds）
* 4-Manifolds and Kirby Calculus by Andras I. Stipsicz and Robert E. Gompf * Differential Manifolds by Antoni A. Kosinski * Introduction to Smooth Manifolds by John M. Lee
我最初是通过约翰·M·李的《光滑流形导论》来学习流形的。这本书内容密集但结构精美，逻辑清晰地引导你从基础拓扑过渡到光滑映射和切空间。读它需要高度专注，但每一个定义都在为……铺垫。
I first learned about manifolds through Introduction to Smooth Manifolds by John M. Lee. The book is dense but beautifully structured, guiding you from basic topology to smooth maps and tangent spaces with clear logic. It demands focus, yet every definition builds toward a…
……（沃尔特·鲁丁）- 《偏微分方程》（劳伦斯·埃文斯）- 《流形上的分析》（詹姆斯·芒克勒斯）- 《抽象代数》（戴维·达米特与理查德·富特）- 《代数拓扑》（艾伦·哈彻）- 《光滑流形导论》（约翰·李）- 《可微流形与李群基础》（弗兰克·华纳）- 《伽罗瓦理论》（哈罗德·爱德华兹）- 《有限群的线性表示》（让-皮埃尔·塞尔与伦纳德·斯科特）……
…(Walter Rudin) - Partial Differential Equations (Lawrence Evans) - Analysis On Manifolds (James Munkres) - Abstract Algebra (David Dummit and Richard Foote) - Algebraic Topology (Allen Hatcher) - Introduction to Smooth Manifolds (John Lee) - Foundations of Differentiable Manifolds and Lie Groups - (Frank Warner) - Galois Theory (Harold Edwards) - Linear Representations of Finite Groups (Jean-Pierre Serre and Leonhard Scott)…
赞同 Munkres 那本。作为后续进阶，还推荐哈彻的《代数拓扑》（他的网站上免费提供）以及李的《光滑流形导论》。
+1 on munkres. Also recommend Algebraic Topology by Hatcher as a followup (free on his website) and Introduction to Smooth Manifolds by Lee.
……刷完小 Rudin（Baby Rudin）。对于拓扑学，具体可以看 Munkres 或者 J·李的《拓扑流形导论》。> 测度论 陶哲轩有本关于这门课的好书。> 微分几何 J·李的《光滑流形导论》> 概率论 《概率论》，Achim Klenke 著 > 博弈论 《博弈论》，Maschler、Solan 和 Zamir 著
…through Baby Rudin. For topology specifically you can look into Munkres or Introduction to Topological Manifolds, J Lee. > Measure Theory T. Tao has a good book on this topic. > Differential Geometry Introduction to Smooth Manifolds by J Lee > Probability Probability Theory, Achim Klenke > Game Theory Game Theory by Maschler, Solan & Zamir
这个建议太棒了。我其实是先从《拓扑流形》（Topological Manifolds）入门，然后再看《光滑流形导论》的，这确实帮我打下了扎实的基础。我之前没读过杜利民（Loring Tu）的书，不过既然我一直想用更清晰、更轻松的方式重温这个主题，那就找来看看。
That's a great suggestion. I actually started with Topological Manifolds before moving on to Introduction to Smooth Manifolds and it really helped build a solid foundation. I havent read Loring Tus books before but let me look at them since I have been wanting to revisit the topic with a clearer and more relaxed approach.