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ALEJANDRIA · BOOK 01 Theoretical Foundations of LLMs A conceptual introduction to Large Language Models 16 MODULES PT/ES/EN
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Book 01 · Digital book

Theoretical Foundations of LLMs

Understand why AI errs with confidence and know when to trust, verify, or intervene.

16 modules · PT / ES / EN · no programming required

Edition 2 · see what's new

From token to agent

AI already writes, decides, and advises alongside you, and it does so with the same confidence whether it is right or making things up. What separates those who use it well from those who merely trust it is one thing: understanding what happens inside. This book rebuilds, from a conceptual perspective, the mechanisms that underpin Large Language Models (LLMs) and the systems built on them, from token to agent. It is not a manual of tools, which change every month, but a theoretical foundation of the principles that endure. By understanding why a model answers the way it does, and where it fails, you trade blind faith for judgment: you know when to trust the output, when to verify, and when to intervene. It is that critical reading, not the prompt trick of the moment, that turns AI from a black box into a tool you command.

Who it's for

For people who use AI in decisions that carry weight.

Technical professionals, researchers, consultants, analysts, and managers who apply LLMs to work with real impact, where a wrong answer is costly and the judgment of when to trust, verify, or intervene makes the difference. If you rely on AI to build, decide, or advise, this book gives you the foundations to do it with judgment, not on faith.

Key concepts

The vocabulary you will master.

LLM Tokens Transformers Attention Embeddings Neural Networks RAG Prompt Agents MCP Skills Context Fine-tuning Q · K · V Multimodality Hallucinations Deep Learning Machine Learning Vectors Quantization Context Window Inference Safety Temperature

Book program

16 modules, from token to agent.

  1. 01What is Artificial Intelligence
  2. 02Information Representation
  3. 03Neural Networks
  4. 04Transformers
  5. 05How an LLM Learns
  6. 06How an LLM Generates Responses
  7. 07Fundamental Limitations
  8. 08Evaluation and Efficiency
  9. 09Prompt and Context Engineering
  10. 10RAG and GraphRAG
  11. 11AI Agents
  12. 12Integration and Interoperability
  13. 13Economics and Strategic Decision
  14. 14Security and Human-AI Collaboration
  15. 15Multimodality
  16. 16Synthesis: The Modern AI Architecture

+ Trilingual glossary · Consolidated references · About the author

Inside the book

How an LLM thinks, makes mistakes, and evolves.

The word "sat" asks (query) and each word answers (key); the weight weights the values (value) the cat sat on mat query k,vk,vk,vk,v 0.50 0.08 0.12 0.30 attention weights (sum to 1): "sat" looks more at "cat" and "mat" new representation of "sat" sum of values, weighted by the scores All of this is computed for every word at once, in parallel.

Module 4: Self-Attention and Q-K-V from the inside

Question becomes a vector(embedding) Vector databasefinds the nearest relevant chunks(top-k documents) Context = question + chunksaugmented short-term memory LLM generates grounded answer The answer is supported by verifiable fragments, which reduces hallucinations and allows citing the source.

Module 10: RAG: retrieve before answering

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