There a very few free audio recording and editing software that I'd recommend. However on the merits of having used it in some of its previous versions there is a particular app that I would recommend without reserve going by the name of Audacity.  The main reason being that its comprehensive and capable set of audio recording and editing features that are very much comparable to other premium alternatives. Purely as an audio recording and editing application its very powerful and is easy enough to get straight into, however it does lack midi features such as midi recording/playback/sequencing in its unmodified state. This also means it doesn't allow you to use midi instruments or midi controller assignment. Consequently it also means it also doesn't have midi sync and midi quantize features either. But! There are mod's (since its an open source project) that can add midi sequencing capabilities and features to it if you're willing to go the lengths needed to do it. 

Ok, so it might not look very polished as far as its skinning and overall product image goes. But it does the job of audio recording and editing very well whether that be single track or multi-track. You can get it now for Windows, Mac and Linux by clicking here.