The crafting system is devilishly brilliant, it's simple to learn and you'll be churning out new equipment, weapons and other ingredients in no time. But be prepared to lose hours of time once you really get into the nuances of it, as creating the perfect version of a weapon for your playstyle requires a lot of time and commitment.
So for folks who've never touched an Atelier game, allow me to try to (albeit badly) explain how the crafting system actually works.
So to make an item, first, you need a recipe for it. You cannot just guess and create something by luck. Most of the basic recipes you get via the main storyline.
An item recipe is made up of various interconnected slots. Each slot accepts either a specific ingredient or any ingredient of a specific type (e.g. 'fire type'). Each slot once filled, will imbue the item you are creating with certain stats, passive abilities or even new skills you can activate.
As these slots are interconnected, you can't just fill the ones you want right off the bat. You always start with just the one central slot, then branch out from there towards the ones you want to reach.
The tricky part is, based on your alchemy level, you're only allowed to put a limited number of ingredients into each recipe. So you'll spend quite a bit of time just trying to solve the puzzle of how to reach the slots you want, at your current alchemy level, with just the ingredients you have collected so far.
Item recipes often have special slot, which if you reach them, will evolve that item into its next form, once you've crafted that evolved form once the hard way, you unlock it's recipe so you can make it directly in the future.
But wait! there is one more level of depth to all this - and this one is the kicker.
It's not just the resources you gather that go into recipes, it's often other craftable materials. So towards the end of the game when you want to make some of the higher-end weapons, you'll need to farm about 20 different ingredients, then craft those into 5 different items, which can then be used to finally craft the weapon you wanted. Phew.
But often you'll find that despite it being an end-game weapon, it may not have a slot in its recipe to unlock your favorite skill or buff. you can, however, create one of its ingredients with that buff, then when you use that ingredient to make the weapon, you can choose to pass that along to the final item. So once you really dig deep into wanting to min/max your items, you realize you can create an almost infinite number of permutations of any weapon by considering not just how you craft the weapon, but how you craft its ingredients.
Thankfully you can complete the game without having to take things to this degree of complexity, but personally, I find it really rewarding having a long-term plan for a specific weapon/skill combination I want and spending a few play sessions making it into a reality.