❡ Book Recommendations

What makes a book good?

Although I like books that have a more didactic character, I believe that the value of a good book lies in its ability to raise more questions than it answers. (Hopefully, after some careful reading, the question is not "why was this book written?"...)

In English:

• A Course in Abstract Harmonic Analysis, Gerald B. Folland (CRC Press)
• A Course in the Theory of Groups, Derek J. S. Robinson (Springer)
• Algebraic Geometry, Robin Hartshorne (Springer) (Also, check the lectures of R. Borcherds, 3 parts)
• Algebraic Topology, Allen Hatcher (Cornell Univ.)
• An Introduction to Differential Geometry and Riemmanian Manifolds, William M. Boothby (Academic Press)
• Analysis on Manifolds, James Munkres (Addison-Wesley Publishing Company)
• Chern Classes: Topological and Geometric Approach, Lukas Bertsch (University of Vienna)
• Differential Geometry, Kühnel Wolfgang (AMS, Student Mathematical Library Vol. 77)
• Elliptic Systems of Phase Transition Type, Nicholas D. Alikakos, Giorgio Fusco, Panayotis Smyrnelis (Birkhäuser)
• Fractals in Probability and Analysis, Bishop Christopher, Peres Yuval (Cambridge University Press)
• Hyperbolic Geometry, Brice Loustau
• Geometry in a Fréchet Context, C. T. Dodson, G. Galanis, E. Vassiliou (Cambridge University Press)
• Introduction to Riemannian Manifolds, John M. Lee (Springer)
• Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, D. H. Sattinger, O. L. Weaver (Springer)
• Mathematical Game Theory, Ulrich Faigle (World Scientific)
• Measure Theory and the Fine Properties of Functions, Evans L.C., Gariepy R.F. (CRC Press)
• Measure, Topology, and Fractal Geometry, Gerald Edgar (Springer)
• Optimal Transport for Applied Mathematicians, Filippo Santambrogio (Birkhäuser)
• Partial Differential Equations, Evans Lawrence C. (AMS)
• Quantum Physics, Steven Casiorowicz (John Wiley & Sons)
• Quantum Theory for Mathematicians, Brian C. Hall (Springer)
• Real Analysis, Gerald B. Folland (John Wiley & Sons)
• Riemmanian Geometry, Manfredo P. do Carmo (Birkhäuser)
• Selected Topics in Infinite Dimensional Topology, Czesław Bessaga, Aleksander Pełczyński (Polish Scientific Publishers)
• Stable Solutions of Elliptic Partial Differential Equations, Louis Dupaigne (CRC Press)
• The Mathematical Theory of Dilute Gases, Carlo Cercignani, Reinhard Illner, Mario Pulvirenti, (Springer, Applied Mathematical Sciences 106)
• The Ricci Flow - An Introduction, Bennet Chow, Dan Knopf, (AMS, Mathematical Surveys and Monographs Vol. 110)
• Tilings and Patterns, Grunbaum B., Shephard G.C. (W.H. Freeman and Company New York)

In French:

• Analyse Fonctionnelle, Haïm Brezis (Dunod)
• Transport et diffusion, Grégoire Allaire, Xavier Blanc, Bruno Despres, François Golse (Les éditions de l'école polytechnique)

In Greek:

• Διαφορικές Μορφές, Manfredo P. do Carmo (Leader Books)
• Διαφορική Γεωμετρία, Αθανασόπουλος Κωνσταντίνος (Παν. Κρήτης)
• Εφαρμοσμένα Μαθηματικά, David Logan (ΠΕΚ)
• Μια Εισαγωγή στη Μαθηματική Βιολογία, Γιαλελής Νικόλαος, Μπιτσούνη Βασιλική, Στρατής Ιωάννης (Κάλλιπος)
• Στατιστική Φυσική και Θερμοδυναμική, Ι. Δ. Βέργαδος, Ι. Ν. Ρεμεδιάκης, Η. Τριανταφυλλόπουλος (Συμεών)
• Στοιχεία Ευκλείδου του Αλεξανδρέως (απόδοση στη σύγχρονη μαθηματική γλώσσα), Ροκοπάνος Νίκος, Σακελλάρη Στέλλα, Τσολομύτης Αντώνιος (Παν. Αιγαίου)
• Στοιχεία Προβολικής Γεωμετρίας, Βασιλείου Ευστάθειος (Συμμετρία)