我还没彻底啃完，但我读 John Baez 的《Gauge Fields, Knots, and Gravity》[1] 读得非常过瘾。[1]: http://www.worldscientific.com/worldscibooks/10.1142/2324
I haven't fully worked through it yet, but I've been really enjoying reading John Baez's Gauge Fields, Knots, and Gravity [1]. [1]: http://www.worldscientific.com/worldscibooks/10.1142/2324
……Spivak 的《流形上的微积分》，但这书从来没真正对过我的胃口。如果你有物理背景，那么 Nakahara 的《Geometry, Topology and Physics》和 Baez 与 Muniain 的《Gauge Fields, Knots and Gravity》结合起来可能会很不错（我没把相对论教材算进来，因为我假设如果你有广义相对论背景，微分几何知识就足够了）。一个我认为非常棒的冷门推荐是……
…Spivak's 'Calculus on Manifolds' but this never really did it for me. If you have a background in physics then some combination of Nakahara's 'Geometry, Topology and Physics' and Baez and Muniain's 'Gauge Fields, Knots and Gravity' might be good (I haven't included relativity textbooks as I assume it you have a background in GR then you have enough differential geometry). An unusual recommendation that I think is really nice is…
……在很大程度上参考了以下教材：-《Algebra: Chapter 0》（Aluffi）-《Real Mathematical Analysis》（Pugh）-《Mathematics and its History》（Stillwell）-《An Introduction to Manifolds》（Tu）-《Gauge Fields, Knots and Gravity》（Baez）-《A First Look at Rigorous Probability Theory》（Rosenthal）-《All of Statistics》（Wasserman）。有几位作者我很信赖，只要主题稍微对点胃口我就乐意掏钱：VI Arnold、……
…following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics (Wasserman) There are some authors I trust and am happy to buy so long as the topic vaguely interests me: VI Arnold,…
作者之一 Baez 写过一本《Gauge Fields, Knots, and Gravity》，对于拓扑在数学物理中的应用来说，这是一本非常优秀、便宜且通俗易懂的入门书。如果你发现自己对这些感到好奇，值得翻一翻。
One of the authors, Baez, wrote "Gauge Fields, Knots, and Gravity" a lovely, cheap, and fairly accessible intro to applications of topology in mathematical physics. Worth a glance if you find yourself wondering about all this
我觉得把纽结作为万物基础的想法经历了几起几落。其中一次是在 90 年代，多亏了 John Baez 和 Javier P Muniain 写的神作《Gauge Fields, Knots and Gravity》，它是“纽结与万物系列”[1] 的一部分，我就是在那时了解到这一点的。那些想法真的很引人入胜。[1] https://www.worldscientific.com/series/skae
I think the idea of knots as a basis for everything has come and gone several times. One of those were in the 90s, which is when I became aware thanks to the excellent "Gauge Fields, Knots and Gravity" by John Baez and Javier P Muniain, that was part of the "Series on Knots and Everything" [1]. Those are really intriguing ideas. [1] https://www.worldscientific.com/series/skae
我还没彻底啃完，但我读 John Baez 的《Gauge Fields, Knots, and Gravity》[1] 读得非常过瘾。[1]: http://www.worldscientific.com/worldscibooks/10.1142/2324
I haven't fully worked through it yet, but I've been really enjoying reading John Baez's Gauge Fields, Knots, and Gravity [1]. [1]: http://www.worldscientific.com/worldscibooks/10.1142/2324
……Spivak 的《流形上的微积分》，但这书从来没真正对过我的胃口。如果你有物理背景，那么 Nakahara 的《Geometry, Topology and Physics》和 Baez 与 Muniain 的《Gauge Fields, Knots and Gravity》结合起来可能会很不错（我没把相对论教材算进来，因为我假设如果你有广义相对论背景，微分几何知识就足够了）。一个我认为非常棒的冷门推荐是……
…Spivak's 'Calculus on Manifolds' but this never really did it for me. If you have a background in physics then some combination of Nakahara's 'Geometry, Topology and Physics' and Baez and Muniain's 'Gauge Fields, Knots and Gravity' might be good (I haven't included relativity textbooks as I assume it you have a background in GR then you have enough differential geometry). An unusual recommendation that I think is really nice is…
……在很大程度上参考了以下教材：-《Algebra: Chapter 0》（Aluffi）-《Real Mathematical Analysis》（Pugh）-《Mathematics and its History》（Stillwell）-《An Introduction to Manifolds》（Tu）-《Gauge Fields, Knots and Gravity》（Baez）-《A First Look at Rigorous Probability Theory》（Rosenthal）-《All of Statistics》（Wasserman）。有几位作者我很信赖，只要主题稍微对点胃口我就乐意掏钱：VI Arnold、……
…following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics (Wasserman) There are some authors I trust and am happy to buy so long as the topic vaguely interests me: VI Arnold,…
作者之一 Baez 写过一本《Gauge Fields, Knots, and Gravity》，对于拓扑在数学物理中的应用来说，这是一本非常优秀、便宜且通俗易懂的入门书。如果你发现自己对这些感到好奇，值得翻一翻。
One of the authors, Baez, wrote "Gauge Fields, Knots, and Gravity" a lovely, cheap, and fairly accessible intro to applications of topology in mathematical physics. Worth a glance if you find yourself wondering about all this
我觉得把纽结作为万物基础的想法经历了几起几落。其中一次是在 90 年代，多亏了 John Baez 和 Javier P Muniain 写的神作《Gauge Fields, Knots and Gravity》，它是“纽结与万物系列”[1] 的一部分，我就是在那时了解到这一点的。那些想法真的很引人入胜。[1] https://www.worldscientific.com/series/skae
I think the idea of knots as a basis for everything has come and gone several times. One of those were in the 90s, which is when I became aware thanks to the excellent "Gauge Fields, Knots and Gravity" by John Baez and Javier P Muniain, that was part of the "Series on Knots and Everything" [1]. Those are really intriguing ideas. [1] https://www.worldscientific.com/series/skae
如果你确实想学几何表述，那么《Gauge Fields, Knots and Gravity》的第一部分是非常好的资源（而且带习题！）。
If you do want to learn the geometric formulation, part 1 of Gauge Fields, Knots and Gravity is a good resource (and has exercises!).