You can adjust the Clip Volume Envelope to reduce the amplitude in specific sections of a clip. On each clip is a yellow line approx. 1/3 from the top. Hover your mouse over this line and you should see the cursor change to an arrow with a "+" at the tail, indicating you can drop a keyframe at this position. Click to create a keyframe at the start, and another at the end of the region you wish to adjust the levels, then create two more keyframes between these two and drag them down a bit to reduce the level in this region.
Thanks for the response, however the keyframe method seems extremly time consuming considering I would like to remove the sound of the Narrator's breath between each sentence in a rather lengthy course. Is there a more efficient less time consuming way?
If there is enough difference in level between the wanted speech and unwanted breaths then using an something like the Compander preset in Amplitude and Compression/Dynamics Processing may help. But you will have to tweak to suit your audio.
Just to expand on what Ryclark said, the Compander preset will be basically acting as a gate on you track, muting the track below a certain level. You'll have to adjust the point at which this happens to get rid of the breaths but allow the actually speech through. In practice this will mean adjusting the position of the preset point between segments 2 and 3 on the graphical display, and possibly adjusting the slope of segment 3.
However, it it was me I wouldn't discount Durin's suggestion of doing it manually with volume envelopes. It's one of those things that sounds complicated when you read it but is very quick to do. It would likely take me under 5 seconds per breath to adjust this way. The other advantage is that you can control the amount of reduction for each breath--unless you're trying to emulate a studio voiceover, a bit of breath left will probably sound more natural than totally muting it.
I've had to do similar things to mixes all too often and generally find that it's faster to just dive in and use envelopes than to spend ages messing with settings trying to find an automatic compander/gate that does what I want to the breath sounds without clipping some of the wanted audio.