user80875: I've read through some explanations saying that every client in the network knows every transaction because when someone wants to perform a transaction, he sends that informationen (how much, to whom and his own address) to everybody he knows and everybody they know and every.... and so on. Until it gets confirmed by everybody in the network. Then the transaction can take place. So everybody in the network knows that this transaction happens, and add the new block to their chain.
Does REALLY everybody have the whole history of transactions (a.k.a one HUGE chain of blocks) stored on their (lets say) computer?
Really all? Isn't this amount of bytes too much for normal hard disks (in my computer, smartphone, ...) considering ALL transactions which have ever happened and happen?

user-1: Depends on which kind of wallet an user is using.
There are two type of Bitcoin wallets available, classified by the way in which they connect to the blockchain and verify that it is the longest and thus the correct chain to follow:

Core Wallet ( example: https://bitcoin.org/en/wallets/desktop/windows/bitcoincore/) which requires to download the whole blockchain, so that every node running this kind of wallet has the full blockchain data stored locally.

Otherwise there are SPV wallets:

Simplified Payment Verification:


A Bitcoin implementation that does not verify everything, but instead
  relies on either connecting to a trusted node, or puts its faith in
  high difficulty as a proxy for proof of validity. BitCoinJ is an
  implementation of this mode.


http://en.bitcoin.it/wiki/Scalability#Simplified_payment_verification
http://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29

MultiBit, Bitcoin Wallet for Android, and Electrum are examples of SPV clients.
some creds to Stephen Gornick

user80276: Everyone running a bitcoin Core node must download the entire ledger of transactions listed on the blockchain... But the vast majority of Bitcoin wallets are simply a place that stores a user's private key and allows users to interact with the network. When someone sends a transaction from their wallet, it gets broadcast to the network and eventually to Bitcoin miners. 
Once a miner finds the next block (that includes your transaction), the solution gets broadcast to the network and those that are running the full Bitcoin Core software incorporate that block into the blockchain.
So although not everyone needs to download the full bitcoin blockchain, there are still a very large number of people who do, and by doing so, secure the network.

80875: <p>I've read through some explanations saying that every client in the network knows every transaction because when someone wants to perform a transaction, he sends that informationen (how much, to whom and his own address) to everybody he knows and everybody they know and every.... and so on. Until it gets confirmed by everybody in the network. Then the transaction can take place. So everybody in the network knows that this transaction happens, and add the new block to their chain.</p>

<p>Does REALLY everybody have the whole history of transactions (a.k.a one HUGE chain of blocks) stored on their (lets say) computer?</p>

<p>Really all? Isn't this amount of bytes too much for normal hard disks (in my computer, smartphone, ...) considering ALL transactions which have ever happened and happen?</p>
 -1: <p>Depends on which kind of wallet an user is using.</p>

<p>There are two type of Bitcoin wallets available, classified by the way in which they connect to the blockchain and verify that it is the longest and thus the correct chain to follow:</p>

<ul>
<li><strong>Core Wallet</strong> ( example: <a href="https://bitcoin.org/en/wallets/desktop/windows/bitcoincore/" rel="nofollow noreferrer">https://bitcoin.org/en/wallets/desktop/windows/bitcoincore/</a>) which requires to download the whole blockchain, so that every node running this kind of wallet has the full blockchain data stored locally.</li>
</ul>

<p>Otherwise there are SPV wallets:</p>

<ul>
<li><strong>Simplified Payment Verification:</strong></li>
</ul>

<blockquote>
  <p>A Bitcoin implementation that does not verify everything, but instead
  relies on either connecting to a trusted node, or puts its faith in
  high difficulty as a proxy for proof of validity. BitCoinJ is an
  implementation of this mode.</p>
</blockquote>

<ul>
<li><p><a href="http://en.bitcoin.it/wiki/Scalability#Simplified_payment_verification" rel="nofollow noreferrer">http://en.bitcoin.it/wiki/Scalability#Simplified_payment_verification</a></p></li>
<li><p><a href="http://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29" rel="nofollow noreferrer">http://en.bitcoin.it/wiki/Thin_Client_Security#Simplified_Payment_Verification_.28SPV.29</a></p></li>
</ul>

<p><a href="http://multibit.org/" rel="nofollow noreferrer">MultiBit</a>, <a href="https://play.google.com/store/apps/details?id=de.schildbach.wallet&amp;hl=en" rel="nofollow noreferrer">Bitcoin Wallet for Android</a>, and <a href="https://electrum.org/" rel="nofollow noreferrer">Electrum</a> are examples of SPV clients.</p>

<p><em>some creds to Stephen Gornick</em></p>
 80276: <p>Everyone running a bitcoin Core node must download the entire ledger of transactions listed on the blockchain... But the vast majority of Bitcoin wallets are simply a place that stores a user's private key and allows users to interact with the network. When someone sends a transaction from their wallet, it gets broadcast to the network and eventually to Bitcoin miners. </p>

<p>Once a miner finds the next block (that includes your transaction), the solution gets broadcast to the network and those that are running the full Bitcoin Core software incorporate that block into the blockchain.</p>

<p>So although not <em>everyone</em> needs to download the full bitcoin blockchain, there are still a very large number of people who do, and by doing so, secure the network.</p>
