Although your cat may act independent and be litter-trained they still rely on you for regular veterinary care, safe shelter, water, food and etc. By taking care of there essential needs you'll be in a much better place to develop a rewarding and mutual relationship. Make sure you get a collar and ID tag for your cat that includes your telephone number, address and name. Remember that there is always a chance your cat may get outside and having the collar and id tag will heighten the chances of your cat returning home safely.
Make sure to attend to all local and county cat registration laws. By insuring your cat is licensed you will be protecting your cat and people in the community. This process is a identification and registration system that is administrated by most local governments.
Your cat should be taken for regular check-ups to the veterinarian. If you are not sure where to take them for this then ask a pet-owning friend or local animal shelter for a referral.
Make sure you provide your cat constant access to fresh water and a nutritionally balanced diet. If you have any doubts about what to do then do not hesitate to consult your veterinarian for advice on how often to feed your cat and what to feed them.
Your cat should have time set aside to be played with. By enjoying regular play sessions with your cat you will be providing physical exercise and mental stimulation.
In closing just remember to be patient and loyal with your cat. Also remember that the majority of behavior problems can be resolved and make sure you have the reasonable expectations of your cat. Contact the local animal Shelter or veterinarian if you have issues with your cat's behavior if you are struggling with your pet's behavior.