This is a purely commuting issue.
I have an around 3km route to the office, and a regular backpack (laptop, accessories, notebooks, ...) which is not a problem to carry around during autumn and winter months, but in the summer the back of my shirt quickly becomes sweaty from carrying it, and carrying it only on one shoulder isn't so good stability wise, while on the road.
I'm looking for advice, what would be a good way to mount it to a bike, or securing it in some way so it lasts throughout the trip, so I don't have to carry it on me.
I've tried securing it to my rear rack with "bungee ropes" (those elastic ropes), but it tends to slip to the side during the ride, and I'm afraid it might fall down.
Bike: Author Reflex SX trekking, with rear rack installed.
Edit (Clarification of what I'm looking for): Solutions for carrying regular rucksacks, like baskets that can be secured to rear rack, or side baskets (I've yet to see examples of those), or some solutions that would enable securing a backpack directly to a rear rack, but in a way that enables me to quickly clamp/unclamp it. I'm also not interested in buying specialized bike backpacks/panniers, but wish to carry my current one.