Lots of good advice in this thread, however a few more pointers :-
1) Earth lead ideally should be one continuous wire – at least 10mm; routing should be battery, bodywork to engine block. As others have said make sure all the connection points are clean, bare metal to metal and tight.
2) Is the thick cable battery positive to the solenoid tight and clean on the solenoid?
It is or was common for the low power and charge cables to connect at the solenoid.
3) Is the Alternator drive belt tight? Clean and not greasy? Is the pulley tight?
4) Is the connector in the back of Alternator and the connections inside clean and on tightly? The ‘sense’ lead is in that connector and if that is not clean then it could be affecting the output of the alternator.
As a suggestion try taking it off and on a few times just to clean up the connections.
If the alternator is sensing the voltage incorrectly it could be overcharging the battery that without some expensive test kit (which few if any garages will have) it is not easy to tell apart from batteries that ‘die’ frequently. Does the battery look to be dry (no fluid in it)? No fluid is a clear sign of overcharging.
5) Is the ‘Battery’ (Ignition) warning light the correct one? The warning lamp is part of the control circuit.
6) Are the battery connections ‘Lug’ (flat, square) or ‘Post’ (round)? With Lug type connections it is easy to connect a battery up the wrong way round – doing that will damage the alternator diode pack and certainly caused reduced charging, that means a new alternator.
7) Is there a spark or flash when the battery is connected or disconnected? If so then there is something draining the battery.
Which leads onto
8) Has someone fitted additional ‘toys’ to the car? (New radio, music amp, alarm which can be draining the battery constantly)