How to measure -15V to 0V using a microcontroller ADC?
You'll need a non-inverting summing amplifier:  



Start with the -15 V at the Vin input. Then the non-inverting input should be at 0 V, so the ratio R1/R2 should be 3/1, like R1 = 30 k&Omega; and R2 = 10 k&Omega;.

If the input voltage is 0 V then with these values the non-inverting input will be at 3.75 V, and we'll choose R3 and R4 to bring that to 5 V. Since the amplification is (R4 + R3)/R3 we can use the same resistor values: R3 = 30 k&Omega; and R4 = 10 k&Omega;. 

Make sure you have an RRIO (Rail-to-Rail I/O) opamp.