iMusic

LindaEB wrote:

Music purchased in iTunes

Is your iPhone logged in with the same Apple ID as the computer for iTunes purchases? If so, your purchases should appear in the Purchased section of the iTunes Store app on your iPhone for you to download. Once downloaded, they should appear in the Music App. click here ➜ Redownload music - Apple Support

or added from my computer does not appear in the "Library" of Music on my iPhone.

Music added from other sources to an iTunes Library on a computer will not appear on an iPhone unless you either sync it directly or are subscribed to Apple Music or iTunes Match services and have the "Sync Library" option turned on for both the computer and the iPhone. This also requires both devices to be using the same Apple ID.

click here for how to directly sync ➡️ Sync music between your Mac and iPhone, iPad, or iPod touch - Apple Support

click here for Windows PCs ➡️ Sync iTunes content on PC with your devices - Apple Support

click here to learn about Apple Music or iTunes Match and the Sync Library function ➡️ Use Sync Library to access your music library across your devices - Apple Support

Perhaps this article will help: If songs are missing from your music library after you turn on Sync Library - Apple Support