Foundations and Financial Instruments
Build the mathematical footing for quantitative work, then use it to understand stocks, bonds, forwards, futures, options, swaps, and credit products.
Part of Quantitative Finance. The online chapters are free to read; the PDF edition is yours to keep, with future updates included.
Build the judgment to work confidently in quantitative finance.
Understand the assumptions behind a pricing model, the evidence behind a strategy, and the limits of a result. The book connects mathematical foundations to practical quantitative work so you can explain your choices and investigate what needs to change.
See what you’ll learnWhat you will learn
- Work with discounting, probability, statistics, linear algebra, calculus, optimization, and numerical methods in financial settings.
- Price and reason about stocks, bonds, forwards, futures, options, swaps, and credit derivatives.
- Connect instrument mechanics to hedging decisions, market conventions, and the risks that appear in practice.
Who this volume is for
- Students, analysts, and practitioners who want one rigorous starting point for the mathematics and instruments used throughout quantitative finance.
Prerequisites: This volume starts with the mathematics. Basic algebra is enough to begin; the calculus, probability, and linear algebra you need are developed along the way.
Volume 1 PDF + code
Own this 883-page edition
Keep the PDF and companion notebooks for offline reading, with future updates included. The corresponding chapters stay free online.
- Carefully typeset PDF
- Companion notebooks included
- Future updates and errata included
- Online chapters remain free to read
Volume 1 of 4 · Available now
$29
one-timeVersion 2026.08.1 · 883 pages · secure checkout via Stripe
Delivered by email · Free updates included
Want the complete library?
Access to every volume, delivered as separate PDFs. Companion notebooks included. Save $37 vs. buying available volumes separately.
Get all-volume access · $79Reader verdict
5.0
out of 5
12 five-star reader reviews
Genuine feedback, with names abbreviated for privacy.
Meet the community“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“Thank you Michael. It's top!”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“Thanks for putting cool stuff out into the world.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
Read all 12 reader reviews
“I would like to thank you for your work. Specifically, the chapter: 'LIME Explainability: Complete Guide to Local Interpretable Model-Agnostic Explanations' was extremely helpful for me in understanding LIME and communicating to colleagues. Your work is inspiring and valuable. Thank you for doing it.”
“Really appreciate the way you have explained the concepts. Simple to understand, yet builds up knowledge exponentially, all while reinforcing it with examples repeatedly. I've read the last two chapters `74.Self-attention & 75.Q,K,V` and I've to admit, my concepts have never been clearer. You really are doing an amazing job breaking down maths and complex concepts like a story!”
“Thanks so much for establishing such an amazing community. I appreciate the opportunity to be a learner and a contributor to the community.”
“I just came across your website where your books are available for free to read. Thank you so much for making this available to the public. This will help a lot of people.”
“I am enjoying reading your writings. I appreciate the effort you put into it. I want to drop a note of thanks. Thank you!”
“Thank you Michael. It's top!”
“Thanks for putting cool stuff out into the world.”
“I found your book Language AI Handbook's explanations of Transformer architectures and production deployment strategies to be exceptionally clear and insightful”
“Your writing feels like a treasure trove of great material. So, thank you for compiling everything on your website!”
“I came across your collection of online handbooks covering quantitative finance, AI, and machine learning. I wanted to reach out and thank you for making such high-quality material openly available. They are incredibly helpful for my CFA Level II review and for brushing up ahead of ML interviews.”
“I read a few of your blogs on NLP and oh WOW, they really are something, now I exactly know how all of the terms Entropy, Cross-entropy and how it is connected to Perplexity, will definitely read more of your blogs.”
“I came across one of your books, Language AI Handbook, and man, I'm loving it. I've read many books but have never found such a comprehensive book on large models that covers everything from start to finish with such depth.”
Exact contents
24 chapters across 4 parts
Every linked chapter is free to read online.
Part I: Mathematical Foundations
- 01Time Value of Money and Interest Rates
Understanding present and future value concepts, compounding, discounted cash flows, and the relationship between interest rates and valuation.
- 02Probability Theory Fundamentals
Basics of probability, random variables, distributions, expected value, variance, conditional probability, and Bayes' Theorem in finance.
- 03Common Probability Distributions in Finance
Key distributions (normal, lognormal, binomial, Poisson, fat-tailed) and their applications in financial modeling and risk management.
- 04Statistical Data Analysis and Inference
Descriptive statistics, estimation concepts, Central Limit Theorem, hypothesis testing, and confidence intervals for financial data.
- 05Linear Algebra for Quantitative Finance
Vectors, matrices, linear equations, and matrix decompositions with applications to portfolio analysis and factor models.
- 06Differential Calculus and Optimization Basics
Derivatives, marginal effects, multivariable calculus, constrained optimization, and convexity in portfolio optimization.
- 07Integral Calculus and Differential Equations
Integrals, continuous compounding, differential equations, and foundations for continuous-time finance models.
- 08Numerical Methods and Algorithms in Finance
Root-finding algorithms, interpolation techniques, and numerical integration for solving financial problems.
- 09Data Handling and Visualization
Importing and managing financial datasets, organizing time series data, and creating effective visualizations.
Part II: Equity and Fixed Income Markets
- 01Equity Markets and Stock Instruments
Stock ownership, market structure, trading mechanics, equity returns, and fundamental market concepts.
- 02Bond Fundamentals and Pricing
Bond types, cash flows, pricing by discounting, yield to maturity, and day-count conventions.
- 03Term Structure of Interest Rates
Yield curves, zero rates, spot rates, forward rates, and bootstrapping techniques.
- 04Bond Risk Measures and Immunization
Duration, convexity, interest rate risk measurement, and immunization strategies for bond portfolios.
Part III: Forwards, Futures, and Options
- 01Forwards and Futures - Instrument Basics
Forward and futures contracts, contract specifications, margin requirements, and market mechanics.
- 02Forward and Futures Pricing and Hedging
Cost-of-carry pricing, arbitrage relationships, and basic hedging strategies using futures contracts.
- 03Commodity Markets and Futures
Commodity market structure, contango and backwardation, convenience yield, and hedging physical commodities.
- 04Foreign Exchange Markets and Currency Forwards
FX market structure, exchange rate quotes, interest rate parity, and currency forwards for hedging.
- 05Option Basics - Calls, Puts, and Payoffs
Call and put options, payoff structures, moneyness, put-call parity, and fundamental option concepts.
- 06Option Strategies and Payoff Combinations
Spreads, straddles, strangles, covered calls, protective puts, and constructing complex payoff profiles.
Part IV: Swaps and Credit Derivatives
- 01Interest Rate Swaps - Fundamentals
Swap structure, fixed-floating exchanges, notional principal, and applications in interest rate management.
- 02Interest Rate Swap Valuation and Applications
Valuing swaps as bond portfolios, swap curves, and practical uses in hedging and synthetic asset creation.
- 03Credit Default Swaps (CDS) and Credit Derivatives
CDS structure, credit risk protection, spread pricing, default probabilities, and recovery rates.
- 04Structured Credit Products (CDOs and Securitizations)
Asset securitization, CDO structures, tranching, credit risk distribution, and valuation challenges.
- 05Convertible Bonds and Hybrid Securities
Convertible bonds as hybrid instruments, conversion features, valuation approaches, and other hybrid securities.
Choose the edition that fits your next step
Volume 1: Foundations and Financial Instruments
883 pages focused on this subject, with future updates included.
$29
Choose this volumeThe complete Quantitative Finance library
All-volume access with separate volume PDFs and future updates. No combined PDF.
$79
Get all-volume accessExplore the other volumes
Volume 2 · 664 pages
Derivative Pricing and Interest Rate Models
Stochastic Calculus · Options · Numerical Pricing · Rate Models
Volume 3 · 770 pages
Econometrics, Portfolio Construction, and Risk
Econometrics · Portfolio Theory · Market, Credit, and Liquidity Risk
Volume 4 · 1011 pages
Quant Trading, Execution, and Deployment
Trading Strategies · Market Microstructure · Backtesting · Production Systems
Author and edition details
About the author and this edition
Michael Brenndoerfer
Michael has spent more than a decade working across software engineering, data, AI, and business. He writes to understand difficult ideas more deeply and to share what he learns in a clear, practical way.
Important: This book is for education and research. It does not provide investment, trading, legal, tax, or other professional advice, and examples are not recommendations.
- Edition
- First edition
- Published
- Last reviewed
Version history
Kept current, not frozen in time
Library access includes every future volume and update. When a volume changes, its updated PDF appears in My books at no extra cost.
Current release
Edition 2026.08.1
Editorial improvements.
Earlier releases2
2026.08.0
Editorial improvements throughout the book, with clearer explanations, refined presentation, improved plots and visualizations, and refreshed companion code.
2026.07.0
Initial complete-book and four-volume PDF release with companion notebooks.