a simple question, is the NXP LPC1768 the best way to learn the ARM CORTEX M3 programming???

A simple question, but like so often, not really a simple answer. The best way to do something is generally not easily defined. The question here is mainly if mbed is the best way to learn it, since the 1768 is the only M3 mbed. Others certainly seem to think so: https://mbed.org/blog/entry/mbed-professional-training-platform/

Personally I think for sure it is a very good platform to learn it on (did it myself). The LPC1768 has a good user manual, which already is really handy if you want to learn the M3 platform on it. Aditionally the mbed environment makes sure you can just write programs without worrying about setting up a toolchain. And finally, the standard libraries allow you to focus on one thing. For example when I wrote an ADC driver library that driver effectively would have been the same as when I would have made it without mbed. However I still used the mbed serial connection, leds, timers, etc.

+1 for me as well. My first Cortex-M3 processor was the mbed-LPC1768 as well. I found it much easier to learn than when I started out several years earlier with the ARM7TDMI based LPC2148 processor and GCC. The mbed device makes it so easy to get started. If something about the mbed SDK and/or online compiler holds you back at a later point in time, you can still use the same device but go down a more advanced path as your skills develop to write drivers without the SDK and/or switch to an offline compiler, etc.

ok I am convinced, thanks :)

It is insightful to read mbed SDK source code and cross-referencing to

• LPC1768 datasheet and user manual
• CMSIS documentation from ARM