user collections

let's say a user can browse an index of products, and they can add the ones they own to their "collection." naturally, there are several editions of some products, so they can select that too. what would be the best/most efficient way to store their collection in a mysql database?

i was thinking of storing a row for each user, and one of the columns would be an array of all the products' unique IDs. is this an acceptable way to do it?

I'm having trouble understanding what you're proposing to me. Would you please draw a diagram to explain your proposal?

table of users, with id
tables of products with id
table of with user id and product id, both foreign keys and shit,
specifies that user x has product y,
niggerth normal form or something