The Middle River is the part of the River Cam that runs through the backs of the Colleges. In the summer it is used almost exclusively for punting. At its upper limit there is a weir and boats cannot pass unless they can be hauled up the special ramp which is fitted with metal rollers. At its lower limit is the lock at Jesus Green which is normally kept padlocked.
It is not widely known, but in the winter (from 31 October to 31 March) it is permitted to navigate a powered vessel along the Middle River. The fee is set in the 1922 River Cam Conservancy Act at one shilling and sixpence. In practice, you simply ring up the Conservators (the phone number is displayed at Jesus Green Lock) and explain that you wish to pass through the lock; they check that your licence is valid, swear you to secrecy and then tell you the combination of the padlocks. They don't ask for the 1/6d. The Conservators like to know what boats are above the lock because they sometimes drain that part of the river so buildings by the river can be repaired. As long as they know you are there, they can warn you in advance.
There are many shallows in the river, particularly beyond Silver Street Bridge.
There are ten beautiful bridges in the mile of river from Jesus Lock to Coe Fen. Some of the bridges are quite small and some are very close together. On your way upstream things are fairly straightforward but on the way back, travelling with the current, things happen rather fast. It's best not to attempt to navigate the backs after a period of heavy rain.
The Mathematical bridge at Queens College is often said to have been designed by Newton. In fact Newton had been dead for twenty years when it was erected in 1749; it was his student Etheridge who deserves the credit. Every piece of wood was in compression and the structure should have held together simply by its own weight. It is said that the iron pins were put in after they had fished all the pieces out of the river.
At the upper end of the Middle River you emerge from under Silver Street Bridge into Coe Fen where you can moor on the common opposite Charles Darwin's house where "The Origin of Species" was written. In priciple, you can continue to along the tiny stream next to Darwin College and reach the Mill Pond. However, I don't think it is deep enough to take a narrowboat.
There is no towpath on the Middle River (historically, the horses waded along a causeway which was built in the middle of the river by the Conservators to break the University's stranglehold over waterway). You can turn a boat in the weir pool at Coe Fen. Keep to the south side of this weir pool - it is very shallow on the north side. When passing Darwin College keep well to the north where the channel is deepest.