In his doctoral thesis, Padilla Gálvez examined central issues of analytic philosophy. His subsequent investigations are characterized by an application of the analytic method to the study of philosophical problems. This method involves both, the analysis of language to eliminate ambiguity as well as a profound scrutiny of the logical form of philosophical propositions. Padilla Galvez's work may be classified into five lines of investigation: philosophy of language, logic, philosophy of history of science, social changes in democratic systems and language for specific purposes. He was dealing with the works of Gottfried Leibniz, Immanuel Kant, Edmund Husserl, Alfred Tarski, Ludwig Wittgenstein, Willard Van Orman Quine, Saul Kripke, among others. Padilla Gálvez is recognized as one of the leading experts of Ludwig Wittgenstein´s philosophy in the English and Spanish-speaking world. As the co-author of the "Wittgenstein Studien" he has published extensively in the field by focusing on logic-grammatical analysis of language. This includes such topics as history of logic and mathematics, Anthropology, language, aesthetics, politics and practical philosophy.
"El Círculo de Viena, reconsiderado". Arbor, 1996, Nr. 612, Tomo CLV, pp. 7– 147.
"Wittgenstein y el Círculo de Viena / Wittgenstein und der Wiener Kreis". Ediciones de la Universidad de Castilla-La Mancha, Cuenca, 1998.
"Wittgenstein, from a New Point of View". Peter Lang, Frankfurt a. M., 2003.
"El laberinto del lenguaje: Wittgenstein y la filosofía analítica / The Labyrinth of Language: Ludwig Wittgenstein and the Analytic Philosophy". Ediciones de la Universidad de Castilla-La Mancha, Cuenca, 2007.
"Idealismus und Sprachanalytische Philosophie". Peter Lang Verlag, Frankfurt a.M., 2007.
"Phenomenology as Grammar". Ontos Verlag, Frankfurt a. M., Paris, Lancaster, New Brunswick, 2008.
"Igualdad en el derecho y la moral". Plaza y Valdés, Madrid, México D.F., 2009.
"Philosophical Anthropology. Wittgenstein's Perspective". Ontos Verlag, Frankfurt a. M., Paris, Lancaster, New Brunswick, 2010. Review: "Notre Dame Philosophical Reviews"
"Wittgenstein: Issues and Debates".. Ontos Verlag, Frankfurt a. M., Paris, Lancaster, New Brunswick, 2010. Review: Derek A. McDougall, Critical notice, British Wittgenstein Society
"Antropología filosófica de Wittgenstein. Reflexionando con P.M.S. Hacker". Plaza y Valdés, Madrid - México, 2011.
"Forms of Life and Language Games".. Ontos Verlag, Frankfurt a. M., Paris, Lancaster, New Brunswick, 2011.
2007. Sobre consistencia y completitud en el sistema axiomático. Discusión sobre la ponencia del Sr. Gödel. Protocolo del 15 de enero de 1931. Mathesis III 21 193-196.
2011. Ludwig Wittgenstein, Nur die Erfahrung des gegewärtigen augenblickes hat Realität’... / Sólo la experiencia del momento actual es real’..., Hat es Sinn zu sagen "zwei Menschen hätten denselben Körper?... / ¿Tiene sentido decir que dos personas tienen el mismo cuerpo?....Dokos. Revista filosófica, Vols. 7-8, 2011, 53-72
2012. Ludwig Wittgenstein, Die normale Ausdrucksweise «Ich habe Zahnschmerzen» / El modo usual de la expresión «tengo dolor de muelas». Dokos. Revista filosófica, Vols. 9-10, 2012, 79-105
2014. Ludwig Wittgenstein, Escrito a máquina . Transl., introduc. and critical notes from Jesús Padilla Gálvez. Editorial Trotta, Madrid, 2014, 692 p..
2016. Ludwig Wittgenstein, Tratado lógico-filosófico / Logisch-philosophische Abhandlung. Ed. from TS 204, Transl., introduc. and critical notes from Jesús Padilla Gálvez. Tirant Humanidades, Valencia, 2016, 250 p..
2017. Ludwig Wittgenstein, Investigaciones Filosóficas. Transl., introduc. and critical notes from Jesús Padilla Gálvez. Editorial Trotta, Madrid, 2017. 329 págs..
2017. Ludwig Wittgenstein, Diktat für Schlick - Dictado para Schlick. Transl., introduc. and critical notes from Jesús Padilla Gálvez and Margit Gaffal. Ápeiron Ediciones, Madrid, 2017.,.
2019. Ludwig Wittgenstein, Tratado lógico-filosófico / Logisch-philosophische Abhandlung. 2nd Ed. from TS 204, Transl., introduc. and critical notes from Jesús Padilla Gálvez. Tirant Humanidades, Valencia, 2019, 258 p.
and of numerous articles in Diálogos, Grazer Philosophische Studien, Journal for General Philosophy of Science, Logos, Mathesis, Modern Logic, Philosophia Naturalis, Philosophisches Jahrbuch, Wittgenstein-Studien, Zeitschrift für Philosophische Forschung and other journals and collections.