Hello Susan,

One of the most common maladies of basil in warm, humid weather is downy mildew. From the pictures you shared, it is likely that your basil plant has downy mildew. Here is an article on diseases of basil that describes downy mildew: http://plantclinic.cornell.edu/factsheets/basildiseases.pdf

You can use the description of the fungal disease to confirm that this is what is affecting your plant.

Another article states that it is safe to harvest and use the basil that is not infected. Cut off the worst leaves and harvest the rest of your plant before it is infected by the fungus. https://extension.umd.edu/resource/downy-mildew-basil-home-garden/

Hope this helps.