TBD. A pragmatic guide to manifold wrangling, whatever your formalism.
Key words: Clifford algebra, differential forms…
See also information geometry.
TBD.
Clifford Algebra formalism
Hestenes' school.
 Cavendish laboratory's introduction
 Hestene's most famous bit of rhetoric
 Hestene's most infamous bit of rhetoric
 stack exchange arguments.
Handy texts:
Alan Bromborsky, An introduction to Geometric Algebra and Calculus
Alan Macdonald, Geometric Algebra:
Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering.
Differential forms formalism
 Flanders, Differential forms
 Frankel, the geometry of physics
 Bachman's book (Bach03) seems popular and is free.
 John Baez's high speed introduction
How is tensor?
Baby steps to picking up all the vector space multilinear weirdness I never got around to.
The intersection point of differential geometry and geometric algebra and linear algebra.
Basic tensor handling

Jeremy Kun:
Refs
 Bach03: (2003) A Geometric Approach to Differential Forms
 Macd16: (2016) A Survey of Geometric Algebra and Geometric Calculus. Advances in Applied Clifford Algebras, 1–39. DOI
 LaLD00: (2000) A unified mathematical language for physics and engineering in the 21st century. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 358(1765), 21–39. DOI
 Moor93: (1993) Braids in classical dynamics. Physical Review Letters, 70(24), 3675–3679.
 HeSo84: (1984) Clifford Algebra to Geometric Calculus a Unified Language for Mathematics and Physics. Dordrecht: Springer Netherlands
 Port95: (1995) Clifford algebras and the classical groups. Cambridge ; New York: Cambridge University Press
 WaAS96: (1996) Differential forms in electromagnetic field theory. In Antennas and Propagation Society International Symposium, 1996. APS. Digest (Vol. 2, pp. 1474–1477 vol.2). DOI
 Flan89: (1989) Differential Forms with Applications to the Physical Sciences. Dover Publications
 WaSA95: (1995) Electromagnetic boundary conditions and differential forms. IEE ProceedingsMicrowaves, Antennas and Propagation, 142(4), 326–332. DOI
 WaAr96: (1996) Electromagnetic Green functions using differential forms. Journal of Electromagnetic Waves and Applications, 10(3), 427–438. DOI
 WaSA96: (1996) Electromagnetics made easy: differential forms as a teaching tool. In 2013 IEEE Frontiers in Education Conference (FIE) (Vol. 3, pp. 1508–1512). IEEE
 Chis12: (2012) Geometric Algebra. ArXiv:1205.5935 [MathPh].
 DoFM10: (2010) Geometric Algebra for Computer Science: An ObjectOriented Approach to Geometry. Morgan Kaufmann
 DoLa03: (2003) Geometric algebra for physicists. Cambridge ; New York: Cambridge University Press
 BrRi95: (1995) Geometrical aspects of statistical mechanics. Phys. Rev. E, 51(2), 1006–1011. DOI
 Amar01: (2001) Information geometry on hierarchy of probability distributions. IEEE Transactions on Information Theory, 47, 1701–1711. DOI
 BoWa76: (1976) Introduction to vectors and tensors, Vol 1: linear and multilinear algebra. Plenum Press
 BoWa06: (2006) Introduction to vectors and tensors, Vol 2: vector and tensor analysis
 Hest01: (2001) Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry. In Geometric Algebra with Applications in Science and Engineering (pp. 3–17). Birkhäuser Boston DOI
 Hest03: (2003) Spacetime physics with geometric algebra. American Journal of Physics, 71(7), 691–714. DOI
 LPRS10: (2010) Statistical Learning for Complex Systems an Exampledriven Introduction.
 Laur87: (1987) Statistical manifolds. In Differential geometry in statistical inference (p. 164). JSTOR
 WaSA97: (1997) Teaching electromagnetic field theory using differential forms. IEEE Transactions on Education, 40(1), 53–68. DOI
 Hest91: (1991) The design of linear algebra and geometry. Acta Applicandae Mathematica, 23(1), 65–93. DOI
 Hest88: (1988) Universal geometric algebra.