Calculus

1. MIT 18.01 Single Variable Calculus, Fall 2006

2. MIT 18.02 Multivariable Calculus, Fall 2007

3. Calculus III: Multivariable Calculus (Princeton University)

4. UC Berkeley: MATH 53 - Multivariable Calculus with Edward Frenkel

Linear Algebra 

1. Linear Algebra (UCLA MATH 115B)

2. Linear Algebra (Princeton University)

3. Linear Algebra Done Right

4. Abstract Linear Algebra

Abstract Algebra 

General Abstract Algebra:

1. Abstract Algebra (Gross)

2. Group Theory

3. MATH 113: Introduction to Abstract Algebra (Spring 2020)

Galois Theory:

4. Galois Theory (YouTube Playlist)

5. Galois Theory (University of Edinburgh)

6. MAU34101 - Galois Theory (Trinity College Dublin)

Rings and Modules:

7. Rings and Modules

Advanced Topics:

8. Abstract Algebra

Commutative algebra

1. Commutative Algebra (Playlist 1)

2. Commutative Algebra (Playlist 2)

Representation theory 

1. Introduction to Representation Theory (Spring 2021) - Video Series

2. Introduction to Representation Theory (Spring 2021) - Course Page

3. Representation Theory (YouTube Playlist)

4. MIT 18.715: Introduction to Representation Theory (Fall 2020)

Number theory

Here are the clickable links for the Number Theory resources:

General Number Theory:

1. Number Theory Playlist

2. Recent Developments in Analytic Number Theory

3. Introduction to Number Theory (Berkeley Math 115)

4. Theory of Numbers

5. Number Theory I - Kiran Kedlaya (2020)

6. Number Theory II - Kiran Kedlaya (2021)

7. Math 205 - Topics in Number Theory (UCSD and Online, Fall 2024)

8. 2020 Spring Number Theory

9. 2022 Spring Analytic Number Theory

Advanced Topics in Number Theory:

10. Core Topics in Modern Number Theory (Video)

11. Core Topics in Modern Number Theory (Course Page)

12. Will Sawin - Number Theory Over Function Fields

Modular Forms:

13. Modular Forms (Channel)

14. Modular Forms (Playlist)

Analysis

Mathematical Analysis(all levels of Analysis up to graduate )(Real,Complex,Fourier and Functional)

Real Analysis

Here are the clickable links for Real Analysis resources:

1. Real Analysis (Berkeley)

2. MIT 18.100A Real Analysis, Fall 2020

3. Real Analysis (UCLA Math 131A)

Complex Analysis

1. Complex Analysis (Fall 2020) - Bandeira, ETH Zurich

2. 2020 Fall Complex Analysis (Alex Kontorovich)

3. From Conformal Invariants to Percolation - C. McMullen

4. Stony Brook MAT 627: Topics in Complex Analysis - Conformal Fractals (Ongoing)

5. Complex Analysis (Berkeley)

Functional Analysis

• MIT 18.102: Introduction to Functional Analysis, Spring 2021

Fourier Analysis 

1. MIT 18.103: Fourier Analysis: Theory and Applications (Fall 2020)

2. Fourier Analysis (YouTube Playlist)

3. Classical Harmonic Analysis (YouTube Channel)

PDEs and ODEs

Differential Equations:

1. Differential Equations (YouTube Playlist)

2. MIT 18.03 Differential Equations, Spring 2006

Partial Differential Equations (PDEs):

3. PDEs (4 Courses Up to Graduate Level)

4. ICTP Diploma - Partial Differential Equations - Giovanni Bellettini

5. Partial Differential Equations (YouTube Playlist)

6. Lectures on Partial Differential Equations (YouTube Playlist)

7. Euler and Navier-Stokes Equations (László Székelyhidi)

8. Maria Colombo - Instability and Non-uniqueness for the Euler and Navier-Stokes Equations

Topology 

Modern and Algebraic Topology:

1. Modern Topology (First Semester Topology)

2. Algebraic Topology (Second Semester Topology)

3. MIT 18.905 Algebraic Topology I Fall 2020

Homotopy Theory:

4. Homotopy Theory 1 (Paris)

5. Homotopy II (2020–2021) Paris

Algebraic Topology (Additional Resources):

6. Algebraic Topology 1 (SharePoint)

   • Password: atop1HS20

7. Algebraic Topology 1 (Polybox)

8. Algebraic Topology 2 (SharePoint)

   • Password: atop2FS21

9. Algebraic Topology 2 (Polybox)

10. Algebraic Topology II Spring 2022 (Metaphor)

Geometry 

Algebraic geometry

1. Algebraic Geometry I: Varieties

2. Algebraic Geometry II: Schemes

3. Algebraic Geometry: Extra Topics

4. Algebraic Geometry Lectures

5. Algebraic Geometry Iakerson, Maria (ETH Zurich)

6. Full Course: "p-adic Geometry" by Peter Scholze (2014)

7. Derived Algebraic Geometry (ETH Zurich)

8. Algebraic Geometry (YouTube Playlist)

9. Dustin Clausen and Peter Scholze - Analytic Stacks

Differential Geometry

Differential Geometry & Geometry of Manifolds:

1. Metric Differential Geometry (Spring 2022)

2. Course Document for Metric Differential Geometry

3. Differential Geometry I (Autumn 2023)

4. Bilibili Video for Differential Geometry I Autumn 2023

5. ETH Zurich: Differential Geometry I Autumn 2023 Video

6. Differentiable Manifolds Course Document

7. Ricci Flow (Berkeley)

8. MIT: 18.965 Geometry of Manifolds I (Fall 2020)

9. MIT: 18.966 Geometry of Manifolds II (Spring 2021)

10. Geometry in Non-Positive Curvature and Kähler Groups

Classical Geometry 

1. Ohio University MATH 3110/5110 College Geometry

2. Ohio University College Geometry Course Page

3. Geometry Part 1: Introduction, Axiomatic Systems

4. College Geometry Project (University of Minnesota, 1965-71)

5. Geometry Course Playlist

6. College Geometry

7. Geometry Playlist

8. Hyperbolic Geometry, Köln 2022

Combinatorics Courses:

1. Introduction to Additive Combinatorics (Cambridge Part III course)

2. Topics in Combinatorics (Cambridge Part III course)

3. MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019

Graph Theory Courses:

1. Graph Theory Playlist