My passion for immersive photography has born some years ago on the same wavelength, so after a few researches about nodal point, stitching techniques and gears, I've decided to build my own wood panohead and I started the journey which led to an impressive huge 360° images gallery.
Now you have the chance to travel through these steps together. Some of them could be boring, and probably you already have a good experience with many of the described concepts, so I'll try to be more concise and less theoretical as possible.
I want to highlight that this instructable is not supposed to be a personal gallery of my best work, but my ego didn't let me choose ordinary photos ;-)
The concept behind the spherical panoramas is nothing complicated, this technique is meant to reproduce in virtual reality (VR) the first person view taken in any direction at a certain instant. In simple words you have to take a lot of pictures all around, at full 360° on the horizon and also up (zenith point) and down (nadir point), and merge them into a single image.
Problems appear when you try to merge the pictures together, indeed they have to be warped to match each other. A software could do that easily, but to do that it has to recognize the identical details in different images to overlap them. These identical details are named "control points" (CP). The more you overlap sequential images, the more CP you'll have. To be fair the number of CP is not as essential as their "quality". Years ago I created this panorama of Milan Gallery adding manually 5 CP for each couple of the 16 picture, and the final equirectangular image came out very precise. In case you wondered what equirectangular means, this projection type is the most used way in VR to display a sphere on a plane, and if you'll manage to load it in a panorama viewer it will be certainly supported.
Stitching a set of photos in a uniform single equirectangular image is totally a mathematical issue, and it has been possible thanks to the efforts of Prof. Dr. H. Dersch (who created Panorama Tools) and Andrew Mihal (who created Enblend and Enfuse tools).
If you want to study in depth the subject there are a lot of forums managed by skilled people where you can find really interesting discussions about this process, the most popular are panotools.org and www.kolor.com.