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Esta obra consta de dos volúmenes y está dedicada al álgebra lineal. En el primer volumen se desarrollan las ideas fundamentales, se establecen los principales resultados teóricos y se explicitan los métodos que, derivados del tratamiento teórico, permiten abordar problemas concretos. Todo ello acompañado de ejemplos ilustrativos elaborados con detalle. Es importante señalar que las demostraciones que aparecen en este libro han sido desarrolladas asumiendo que el cuerpo base es de característica cero. Por ello, el lector interesado en trabajar sobre cuerpos finitos debe tener en cuenta que es posible que algunos de los argumentos utilizados tengan que ser adaptados al caso de característica positiva. El segundo volumen se centra en los ejercicios. Así, por cada uno de los capítulos del primer volumen, se presenta una colección extensa de problemas y ejercicios resueltos, tanto de carácter teórico como práctico. Estos dos libros pretenden ser un documento de apoyo al estudio en las asignaturas de álgebra lineal de los primeros cursos de los grados universitarios. El objetivo de esta obra, o al menos esa ha sido nuestra intención, es que pueda ser de ayuda tanto a estudiantes de matemáticas como de ciencias o de ingenierías, ya que el lector puede optar por profundizar tanto como necesite en los razonamientos teóricos o, a partir de las ideas, de los resultados y de los métodos expuestos, y sin entrar en los detalles de las demostraciones, enfrentarse a los múltiples problemas y ejercicios resueltos que se aportan. Esperamos haberlo conseguido. Queremos dar las gracias a nuestra compañera Sonia Pérez Díaz, Catedrática de Universidad de Matemática Aplicada de la Universidad de Alcalá, por la lectura y revisión detallada, así como por sus comentarios, siempre enriquecedores, de las versiones preliminares del libro. Dar las gracias a Sonia también por transmitirnos su entusiasmo con este proyecto. Asimismo, queremos agradecer a todos los discentes que durante años han ido pasando por nuestras aulas en las asignaturas de álgebra lineal y que han contribuido, con sus preguntas e inquietudes, a la concepción de este libro. Los Autores.