I have always used the Uni Knot with a double line and 6 turns for mono (12 turns for braid, Yes, 12!). Lubricate well with saliva ...

Recently heard about the Centauri Knot (do a Google search) after hearing great reports about it from the Saltwater guys (very popular in South Africa and Australia). It's a low-friction, high-strength knot and easy to tie. (Also works with nylon coated wire without kinking if you are careful ...)

Boost knot strength by doubling the line you use to tie the knot. I have not lost a fish in fresh or salt due to knot failure for almost as long as I can remember after doubling the line (and using the Uni) ...

For joining lines, braid to mono (or flouro), try the following: Mono or fluoro single line onto double braid with the Centauri Knot (standard 3 turn Centauri) - double braid 12 turn uniknot onto the single mono or fluoro. As always, lubricate well with saliva, tighten carefully as usual and trim the tag ends ... This join will not let you down, is reasonably small and neat and passes through the guides easily - also the levelwind on your reel if you want to use a longer mono or fluoro leader.

Keep well and good fishing!
:-)
Jacques