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A Greyhound can back out of a standard buckle collar, so you will need to purchase a martingale collar for your new pup. You should never use a metal choke collar as this could damage your Greyhound’s throat.  You can find the leash and the martingale collar at your local pet store. A martingale collar is made up of 2 loops, a large loop that is adjustable and placed around your dog's neck, and a small loop, known as the control loop. The leash is clipped to the D ring on the small loop. When your dog tries to pull his head out of the collar, the tension on the leash will pull the small loop so it is taut, making the large loop smaller and tighter around his neck. This will prevent him from escaping. A big part of training your dog is sticking to a daily walking schedule and using the leash to keep your Greyhound from running too fast or too far without you. Greyhounds hunt by sight and are bred to chase after prey. You will need to keep your Greyhound on a leash whenever he is out of the house or on a walk to keep him from running into the street while on the “hunt” for prey. Make sure you can put 2 fingers under your Greyhound’s collar, this means there is enough slack for it be comfortable but not too much to allow your Greyhound to slip out of the collar. Most Greyhounds are raised in crates and are very comfortable sleeping and relaxing in them. Greyhounds are known to be very clean animals and will likely not go to the bathroom in their crate. When you first bring your Greyhound home, it’s important that you do crate training to allow your Greyhound to get used to his new environment and to establish a training routine. Buy a large crate, at least 42 inches (110 cm), to act as a safe space for your new Greyhound. You should place the crate in a room or area that gets a lot of traffic and family activity. Placing it in a remote location, like a basement or a room at the back of the house can make your Greyhound feel abandoned or ignored. Your Greyhound should see his crate as his safe space, so avoid sending him to his crate as punishment, especially when he first adjusting to his new environment. Rather than scolding him or enforce a harsh punishment, tell your Greyhound a firm “No” in a low voice when he does something wrong. Many newly adopted Greyhounds will go through a honeymoon period, where he acts quiet and controlled for the first week in his new home. Your Greyhounds full personality may not emerge until 8 weeks after he enters your home.  Never leave your Greyhound unattended in your home during the first several weeks of training, especially if he is not yet house trained. If you have to leave your dog unattended, put him in his crate to prevent any accidents.

Summary:
Buy a 6 feet (1.8 m) nylon leash and a martingale collar. Use a crate to house train your Greyhound. Do not use the crate as punishment.