[stochastician]

If, like me, you're not a real mathematician but suffered through linear algebra and differential equations, you can still totally understand this stuff! I started off teaching myself differential geometry but ultimately had far more success with lie theory from a matrix groups perspective. I highly recommend:

https://www.amazon.com/Lie-Groups-Introduction-Graduate-Math...

and

https://bookstore.ams.org/text-13

My friends were all putnam nerds in college and I was not, and I assumed this math was all beyond me, but once you get the linear algebra down it's great!

[voxleone]

My experience with groups and linear algebra is similar. I made real progress only after I got past the initial fear and intimidation, making a point of understanding those beautiful equations. Now I find myself agreeing with those who argue that mathematics education could profitably begin with sets and groups instead of numbers.

https://d1gesto.blogspot.com/2025/11/math-education-what-if-...

[AnotherGoodName]

Super easy to explain sets and groups once you've learnt how modulus works too. Start with the additive group and how it behaves under mod m, then go into the multiplicative group and the differences it has and the show why x^y = 1 mod m for certain values due to behavior of the multiplicative group. It's reasonably easy to grok how those two groups work and this gives people an intuitive understanding for the additive and multiplicative groups and they can go further from there.

I wrote an article targeting the average lay person that teaches this way; https://rubberduckmaths.com/eulers_theorem

Hopefully it's helpful and gives people good intuition for this. Group theory is extremely fundamental and can and should be taught after basic arithmetic and modulus operations. There's really no reason it can't be taught in childhood.

[mejutoco]

I vividly remember first day of school after kindergarten in Spain. (3-4 years old?) Sets and Venn diagrams, how interesting and intuitive. Unfortunately it was arithmetic from then on.

[lebca]

Second this! And if you want a part memoir part history of this subject as it relates to physics (through Langlands Program) part ode to the beauty of maths, I recommend reading Edward Frenkel's Love & Math:

https://en.wikipedia.org/wiki/Love_and_Math

and if you went to school in maths but now have left that world, this book engenders an additional spark of nostalgia and fun due to reading about some of your professors and their (sometimes very difficult) journey in this world.

[fasterik]

There is also Naive Lie Theory by Stillwell, which is targeted at an undergraduate level. I haven't read it yet, but it's been on my radar for a while.

https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math...

[chombier]

Also check out Jean Gallier's notes (available online) https://www.cis.upenn.edu/~jean/gbooks/manif.html

[senderista]

I recommend this intro graduate text on Lie representation theory:

https://link.springer.com/book/10.1007/978-1-4612-0979-9

[coderatlarge]

for those who need an easier introduction to the subject (no general integration theory required, just finite sums) i can highly recommend

https://link.springer.com/book/10.1007/978-1-4614-0776-8

it doesn’t say what a lie group is but it gets you down the road if understanding representations and what tou can do with them. dramatically easier than fulton and Harris for self-study.