My Mac does not restart when installing the OS X Yosemite v10.10.3 Update?? it just keeps a black screen till I force restart the Mac??

Try booting in Safe Mode

OS X: What is Safe Boot, Safe Mode?

Try resetting the SMC and NVRAM/PRAM

Intel-based Macs: Resetting the System Management Controller (SMC)

About NVRAM and PRAM

Try booting to Recovery and repairing the startup disk

OS X: About OS X Recovery

Last , resinstall Yosemite

OS X Yosemite: Reinstall OS X

Try running the combo update.

10.10.3 Combo Update

Eric Root it is impossible to run the Combo when the Mac does not boot. The OP says " it just keeps a black screen till I force restart the Mac?"

Eric Root wrote:

Try running the combo update.

10.10.3 Combo Update