What is a good non-technical introduction to theories of everything?

The book Out of this world written by Stephen Webb is a good introduction if you have really no idea what modern fundamental physics is up to. It is the one that made me excited about this stuff for the first time several years ago, and the excitement still holds on :-).

It gently starts by explaining why symmetries are important in physics, followed by an overview about QM and GR, what particle physics generally is about, and the standard model. Then the key ideas behind GUTs (Grand Unified Theories), supersymmetry, and extra dimensions leading to supergravity as a first unified theory including gravity, get introduced. The second part focuses on explaining string and M-theory (other approaches are shortly mentioned too) and some topics, such as black holes, the holographic principle, and cosmology that can be addressed by it.

The book builds up the wisdom it explains in a logical and systematic manner and it is written in a absorbing style that made it difficult for me to put it away. Historical notes about when which ideas and concepts are discovered by whom are included and the way the narrator tells the story made me think that these are all nice people who do awesome and cool things when reading it for the first time.

These sorts of questions are hard to answer unless there is some understanding about the level of math and physics the asker actually has. Probably one of the most irritating aspect about trying to learn physics is that there is a lot of literature out there that completely ignores any discussion of the Lagrangian and Hamiltonian which are so fundamental to physics formulations (in fact I have an entire college physics text that doesn't use either term once, which is mind numbing and infuriating in retrospect, and I even had a physics grad argue blue in the face that the Hamiltonian was not $mathcal{H}=T+V$). If a person has not been exposed previously to these concepts, then it is very difficult to have a coherent conversation about physics let alone the Theory of Everything.

Assuming you have at least this level of introductory understanding, the next place I would start is to get an understanding of algebra, lie groups and the standard model. The best introductory paper I have ever read is A Simple Introduction to Particle Physics by Robinson, Bland, Cleaver and Dittman of Baylor University. I would focus especially on Part II - Algebraic Foundations.

The reason this is critical is that although the Theory of Everything is not some sort of crude algebra (despite attempts by some to make it so), modern physics is understood in the language of algebra, and even more importantly a supersymmetry algebra which makes us of Grassmann numbers for the fermionic fields.

Another good introductory text which is worth exploring is the book Lie Groups, Physics and Geometry by Robert Gilmore. I would pay special attention to chapter one, as there is an excellent discussion of why the general polynomial of degree 5 or more can not be solved using radicals. It also gives an excellent initial expose about Lie groups and their classification as simple vs. solvable.

In any case, if you want to master Theories of Everything, it is the language of algebra that needs to mastered first.

There is one book with a unique title Planets and Electromagnetic Waves which unifies laws in sky and laws for electromagnetic waves, which is somewhat non technical, and which covers the following things.

(1) Existence of atmosphere in planets and capacity of planets to retain atmosphere. (2) Existence of winds in planets and relative speeds of winds in planets. (3) Existence of magnetic fields in self-rotating planets and stars. (4) A definition for black holes with maximum possible temperatures of black holes and a simple derivation for Chandrasekar limit for black holes. (5) Microwave back ground. (6) Gravitational waves and LIGO. (7) Maxwell’s distribution law for black body radiation. (8) An unexpected application of Wien’s displacement law. (9) Method to classify electromagnetic waves as light waves and radio waves. (10) Planck’s equations for light waves and radio waves. (11) Simplified derivation for Einstein’s energy-mass formula. (12) Unexpected connections between laws for sky and laws for electromagnetic waves.

This book is interesting, because it unifies sky and energy waves. But this book does not cover all fundamental aspects of physics.