Re: fourier transform
As you know the fourier transform transforms a time domain signal to the frequenct domain. Doing this you will relax some tedious calculations which would otherwise be done in the time domain. There really is a lot of practical applications for this. For example, in a GSM phone the speech coding makes use of this. However, to understand this fully you have to understand the FFT algorithm which is a clever way of doing a fourier transform in practice.
Generally speaking, I find that the fourier transform (or any other tranform) isn't strange at all. We just happened to be most familiar with signals in the time domain, mainly because the life is a function of time, not frequency. But it could just have been the other way, signals could have been more familiar to us as functions of frequency. Often, the frequency spectrum says a lot more about the signal than the time domain "spectum".