Rather than go on about how safe Paypal is, we've provided a link to their site where they go to great lengths in answering any questions you may have about using the service.
Here's a little section from the Paypal website concerning security
Whether you’re buying, selling, or transferring money, you get an extra layer of security when you use PayPal. That’s because all your financial information (like your credit card number) is securely stored and encrypted on our servers, so you don’t need to share your financial information with the person you’re buying from.
In addition, your transactions are monitored 24 hours a day, seven days a week, by a dedicated team of security specialists. Their mission is to identify suspicious activity and help protect you from fraudulent transactions.
If you ever notice a charge on your account, for something you didn’t authorize, report it immediately. We’ll secure your account and launch an investigation to find out what’s going on. If we find that someone has used your PayPal account without your permission (for example, someone stole your account password), or there was an error (for example, money was incorrectly taken from your account), we’ll cover you for the full amount of every eligible unauthorized transaction.
Finally, if a transaction doesn’t go as planned, or you’re worried about anything at all, like fraud or phishing, we make it easy for you to report issues, and get help. On top of all this, we provide additional protection through our Purchase Protection and Seller Protection programs, described below.
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