What is BH for corners?

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http://www.speedcubing.com/chris/bhcorners.html

Do we have to learn all these 378 algorithms for BH corners or only some of them?

From the site you linked:

The following are all algorithms necessary to use the Beyer-Hardwick method for corners. Please bear in mind that there are often multiple algorithms you could use for a certain case. The case name is more important for each algorithm than the given algorithm. In later pages to follow you will see how to use the case name for a certain cycle to construct the correct algorithm when solving. We include one algorithm for each case merely for completeness.

No, you do not need to learn more than about 10-15 cases, or types of commutators. Read the tutorials linked to in this thread for a further explanation. Sadly, Daniel nor I have had enough to time put together the explanation page we talked about on that site. Byu's tutorial does a very good job of explaining this, and would be a good resource to follow up with.
 
Not too sure but i've been self teaching myself how to permute and oriente (simultaniously) corners aswell as edges using commutators... like, not too sure if I use actual ''pure'' commutators, but i sure and doing XYX'Y' stuff, it's pretty intuitive. I was told it sounded lie BH at some point, but this is much more advanced stuff...
 
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