The Infusions and Artificer knows exist as recipes in an Artificer's LabBook.
The infusions that you add to your labbook as you gain levels reflect the arcane research you conduct on your own, as well as intellectual breakthroughs you have had about the nature of the multiverse. You might find other infusions during your adventures. You could discover an infusion recorded on a scroll or in a dusty tome in an ancient library, for instance.
Copying an Infusion into the Book. When you find an infusion you can add it to your labbook, if it is an infusion, you are high enough level to prepare and if you can spare the time to decipher and copy it.
Copying an infusion into your labbook involves reproducing the basic form of the infusion, then deciphering the unique system of notation used by the artificer who wrote it. You must study the infusion until you understand the mechanisms required, then transcribe it into your labbook using your own notation.
For each level of the infusion, the process takes 2 hours and costs 50 gp. The cost represents material components you expend as you experiment with the infusion to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can use the infusion just like your other infusions. The infusion is essentially added to your "infusions known" and will allow you to exceed the maximum infusions known for your level. You are still limited by the normal limit on "infused items" however.
Replacing the Book. You can copy an infusion from your own labbook into another book, for example, if you want to make a backup copy of your labbook. This is just like copying a new infusion into your labbook, but faster and easier, since you understand your own notation and already know how to use the infusion. You need spend only 1 hour and 10 gp for each level of the copied infusion.
If you lose your labbook, you can use the same procedure to transcribe the infusions you currently have active into a new labbook. Filling out the remainder of your labbook requires you to find new infusions to do so, as normal. For this reason, many artificers keep backup labbooks in a safe place.
The Book's Appearance. Your labbook is a unique compilation of recipes, with its own decorative flourishes and margin notes. It might be a plain, functional leather volume that you received as a gift from your master, a finely bound gilt-edged tome you found in an ancient library or even a loose collection of notes scrounged together after you lost your previous spellbook in a mishap.