Suggested Readings

GENERAL (Books)

R. ABRAHAM, J.E.MARSDEN and T. RATIU : Manifolds, Tensor Analysis, and Applications (2/E), Springer-Verlag, 1988.

GENERAL (Expository papers/Notes/Reports)

M. ATIYAH : What is geometry ?, The Mathematical Gazette 66(1982), 179-184.

S.S. CHERN : From triangles to manifolds, Amer. Math. Monthly 86(1979), 339-349.

S.S. CHERN : What is geometry ? Amer. Math. Monthly 97(1990), 679-686.

R. HOWE : Very basic Lie theory, Amer. Math. Monthly 90(1983), 600-623; Correction, Amer. Math. Monthly 91(1984), 247.

R.S. MILLMAN : Kleinian transformation geometry, Amer. Math. Monthly 84(1977), 338-349.

R.S. MILLMAN and A.K. STEHNEY : The Geometry of Connections, Amer. Math. Monthly 80(1973), 475-500.

GEOMETRIC TRANSFORMATIONS

M.A. ARMSTRONG : Groups and Symmetry, Springer-Verlag, 1988.

R.P. BURN : Groups. A Path to Geometry, Cambridge University Press, 1985.

S.V. DUZHIN and B.D. TCHEBOTAREVSKY : Transformation Groups for Beginners, Amer. Math. Soc., 2004.

M. HENLE : Modern Geometries. Non-Euclidean, Projective, and Discrete (2/E), Prentice Hall, 2001.

P.M. NEUMANN, G.A. STOY and E.C. THOMPSON : Groups and Geometry, Oxford University Press, 2003.

E.G. REES : Notes on Geometry, Springer-Verlag, 2000.

T.Q. SIBLEY : The Geometric Viewpoint. A survey of Geometries, Addison-Wesley, 1998.

P. TONDEUR : Introduction to Lie Groups and Transformation Groups (2/E), Springer-Verlag, 1969.

CLASSICAL DIFFERENTIAL GEOMETRY

L. AUSLANDER : Differential Geometry, Harper & Row, 1967.

M.P. do CARMO : Differential Geometry of Curves and Surfaces, Prentice Hall, 1976.

C.G. GIBSON : Elementary Geometry of Differentiable Curves, Cambridge University Press, 2001.

C.C. HSIUNG : A First Course in Differential Geometry, International Press, 1997.

W. KUHNEL : Differential Geometry. Curves-Surfaces-Manifolds, Amer. Math. Soc., 2002.

J. McCLEARLY : Geometry from a Differentiable Viewpoint, Cambridge University Press, 1994.

R.S. MILLMAN and G.D. PARKER : Elements of Differential Geometry, Prentice-Hall, 1977.

B. O'NEILL : Elementary Differential Geometry (2/E), Academic Press, 1997.

J. OPREA : Differential Geometry and its Applications, Prentice Hall, 1997.

A. PRESSLEY : Elementary Differential Geometry, Springer-Verlag, 2001.

DIFFERENTIABLE MANIFOLDS

W.M. BOOTHBY : An Introduction to Differentiable Manifolds and Riemannian Geometry (2/E), Academic Press, 2003.

L. CONLON : Differentiable Manifolds (2/E), Birkhauser, 2001.

J.M. LEE : Introduction to Smooth Manifolds, Springer-Verlag, 2003.

J. LEE : Manifolds and Differential Geometry, Amer. Math. Soc., 2009.

Y. MATSUSHIMA : Differentiable Manifolds, Marcel Dekker, 1972.

F.W. WARNER : Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, 1983.

MATRIX GROUPS/ABSTRACT LIE GROUPS

A. ARVANITOYEORGOS : An Introduction to Lie Groups and the Geometry of Homogeneous Spaces, Amer. Math. Soc., 2003.

A. BAKER : Matrix Groups. An Introduction to Lie Group Theory, Springer-Verlag, 2002.

J.G.F. BELINFANTE and B. KOLMAN : A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods, SIAM, 1989.

M.L. CURTIS : Matrix Groups (2/E), Springer-Verlag, 1984.

J.J. DUISTERMAAT and J.A.C. KOLK : Lie Groups, Springer-Verlag, 2000.

K. ERDMANN and M.J. WILDON : Introduction to Lie Algebras, Springer-Verlag, 2006.

B.C. HALL : Lie Groups, Lie Algebras, and Representations. An Elementary Introduction, Springer-Verlag, 2004.

J.E. HUMPHREYS : Introduction to Lie Algebras and Representation Theory, Springer-Verlag, 1972.

J.F. PRICE : Lie Groups and Compact Groups, Cambridge University Press, 1977.

W. ROSSMANN : Lie Groups. An Introduction Through Linear Groups, Oxford University Press, 2002.

A.A. SAGLE and R.E. WALDE : Introduction to Lie Groups and Lie Algebras, Academic Press, 1973.

J. STILLWELL : Naive Lie Theory, Springer-Verlag, 2008.

K. TAPP : Matrix Groups for Undergraduates, Amer. Math. Soc. , 2005.

MISCELLANY

R. ABRAHAM and J.E. MARSDEN : Foundations of Mechanics (2/E), Benjamin/Cummings, 1978.

V.I. ARNOLD : Mathematical Methods of Classical Mechanics (2/E), Springer-Verlag, 1989.

A.F. BEARDON : Algebra and Geometry, Cambridge University Press, 2005.

J.J. DUISTERMAAT and J.A.C. KOLK : Multidimensional Real Analysis I. Differentiation, Cambridge University Press, 2004.

T. FRANKEL : The Geometry of Physics. An Introduction (2/E), Cambridge University Press, 2004.

D. HOLM : Geometric Mechanics, I : Dynamics and Symmetry, World Scientific, 2008.

D. HOLM : Geometric Mechanics, II : Rotating, Translating and Rolling, World Scientific, 2008. 

D. HOLM, T. SCHMAH and C. STOICA : Geometric Mechanics and Symmetry, Oxford University Press, 2009.

P. LIBERMANN and C.M. MARLE : Symplectic Geometry and Analytical Mechanics, D. Reidel, 1987.

G.L. NABER : The Geometry of Minkowski Spacetime, Springer-Verlag, 1992.

B. O'NEILL : Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.

M. PUTA : Hamiltonian Mechanical Systems and Geometric Quantization, Kluwer, 1993.

M. REID and B. SZENDROI : Geometry and Topology, Cambridge University Press, 2005.

M. SPIVAK : A Comprehensive Introduction to Differential Geometry (3/E), vol. I-V, Publish or Perish, 1999.

J. STILLWELL : Geometry of Surfaces, Springer-Verlag, 1992.