Foundations and Evolution of NLP: Concepts, Architectures, Techniques, Mathematical Principles and Emerging Paradigms

\textbf{Background:}Natural Language Processing (NLP) has evolved from rule-based and statistical approaches to deep learning, transformer architectures, large language models, retrieval-augmented generation, semantic embeddings, and agent-based systems. These advances have transformed how machines represent, understand, retrieve, generate, and reason over human language. \textbf{Problem \& Objective:}Despite this rapid evolution, the NLP field has become increasingly fragmented across concepts, architectures, mathematical principles, and emerging paradigms. This paper aims to provide a comprehensive technical review of the foundations and evolution of NLP, with particular attention to linguistic foundations, text representation, neural architectures, transformers, language models, embedding spaces, retrieval systems, RAG, model adaptation, and multi-agent paradigms. \textbf{Methods:}This review adopts a structured technical and conceptual approach. It analyzes major NLP techniques from symbolic, statistical, neural, and generative perspectives, while highlighting their underlying mathematical principles, including vector spaces, probabilistic modeling, similarity functions, attention mechanisms, optimization objectives, retrieval scoring, and model adaptation strategies. \textbf{Results:}The review proposes a unified organization of modern NLP technologies, showing how classical linguistic processing evolved toward semantic representation, deep neural architectures, transformer-based models, LLMs, retrieval-augmented systems, and agentic AI. It also identifies key challenges related to hallucination, bias, explainability, privacy, evaluation, computational cost, and low-resource languages such as Malagasy. \textbf{Conclusions:}Modern NLP is no longer limited to text processing; it has become a multidisciplinary ecosystem combining language modeling, mathematical representation, knowledge retrieval, reasoning, and autonomous agentic workflows. This review provides a theoretical and technical foundation for future research in NLP, especially for educational NLP, personalized learning, automatic educational content generation, RAG-based systems, and low-resource language technologies.