Software

Microsoft has a free tool called ORCA that allows you to modify MSI files.  I use it all the time.

http://msdn.microsoft.com/en-us/library/aa370557(v=vs.85).aspx

Orca is pretty much the only free tool out there and is really only used to change a typo in the properties table of an MSI/MST - anything beyond that and it gets crazy confusing for most of us. 

After Orca, you have to "pay to play".  Since Wise Package Studio is dead, AdminStudio from Flexera is pretty much the only tool in the market.  Yes, there are others to choose from, but they have very limited support and not as much capabilities as AdminStudio.  Flexera must have 98.997% of the market and using any other tool is not going to help you learn the details of MSI technology because they have their own propreitary way to creating MSI's which do not conform to the standards Microsoft established 20 years ago.

You could mention MSI Studio, but that only exists as a module within ChangeBASE from Dell Software, so that could be an option if you need to leverage the testing tools offered by CB.

Orca is a bit hard core, but its my choice. What deployment tool are you using? Flexera offer a free 'limited' tool set for SCCM, Altiris & LANDesk. Infopulse have a useful & reasonably priced tool.

Orca is the only free option that allows you to perform low-level MSI editing. Of course, you need to know MSI tables and understand what you do.

Another set of tools include AdminStudio and Advanced Installer. AdminStudio is more powerful, more expensive and more complicated. AdvancedInstaller is the lighter and cheaper option. The recommended MSI Studio seems to be dead from 2011.

I recommend you to start from Orca because it's free, just to understand your goals and formulate your requirements to the commercial editor.