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I'm using the Bitcoin Wallet Client and I've noticed that you could create as many addresses as you want. But I also noticed that there's only 1 Total Amount for the wallet. So does that mean that you could have multiple addresses, but all of that points to same single wallet?

More: And so, if my wallet contains several addresses, when I would like to send coins to another address of another person, do I need to create another address to send the coins? Or do I need to send coins one by one from each address? Or could I just send from one address since all of the addresses are in the same wallet?

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In the Bitcoin protocol and network there is no concept of "wallet" or "account". It only recognizes addresses. Whoever has the key corresponding to an address can spend the coins in it.

A wallet is merely a collection of addresses with their corresponding keys. The Bitcoin-qt client manages for you a wallet file on your computer. Every address in this wallet is spendable by you, so the software displays the total amount in all addresses as your balance. You don't really need to know how many coins are in each address, you just want to know how much you have in total.

I wouldn't say that the addresses "point" to a wallet as that would imply the wallet is a thing on its own. Note that you can have the same address in several wallets, but that's not recommended.

Some other software, such as Multibit, allow you to easily manage several wallet files, and see the total balance for each.

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Yes exactly. If you're using Bitcoin-QT, a wallet contains multiple addresses and therefore private-keys associated to each address. All Bitcoin cares about and knows about are addresses, which might or might not have coins assigned to them.

What the Bitcoin-QT wallet does is it calculates the amount based on all the addresses within it that you own. So yes, you can have a wallet with multiple addresses which all essentially point to a single wallet.

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Each address has a different amount of Bitcoins. Thw Wallet shows you the total, and it allows you to spend from them all at the same time.

But you need to be careful. If you have an address whose money you do not want to mix with that of another one (e.g. one address's money comes from mining and is legal, and another comes from selling marijuana in the Deep Web) you need not to spend bitcoins from these two addresses at the same time, as that will tie them to the same key owner (you).

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Let's go a little to the basics of how Bitcoin actually works. At least in a summarised, high level view. Your Bitcoin address balance is the sum (net) of all the transactions that that originated or terminated at your Bitcoin address. For this reason, anybody on earth, knowing your Bitcoin address, can determine how many Bitcoins you hold.

A Bitcoin address is what is generally called the "public" part of the generated pairs of keys that identify uniquely your deposits. If you were to wonder what I'm talking about, please refer to this document that gives an explanation of it.

Your wallet merely stores these pairs, public and private, and is able to reconstruct the balance of the addresses by navigating through all the transactions of the synchronised blockchain. There is no relation "one wallet - one address / multiple addresses". The wallet is merely a digital container, but a piece of paper with both the public and private keys written on it could be a container too (just a little less useful ;) ).

Hope it clarifies.

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