I really enjoy laying out by the pool and swimming, however my mom doesn't know how to swim. I really think it would be a great family leisure activity we can do together, however she won't venture beyond the the shallow end of the pool. Does anyone have suggestions on how I can ease her fears and teach her to swim? I'm not the best swimmer myself but I can get from one end of the pool to the other. Thanks in advance for your suggestions.

The good news is that you teach adults almost identically to how you teach little kids. Have her start by blowing bubbles. Then have her practice blowing bubbles, lifting up breathing, bubbles, breather, bubbles, breathe, etc.

Then teach her how to float. Then pushing off the wall in a "streamline" (like an arrow or rocketship). Then pushing off in a streamline, and kicking. Then streamline, kick, move her arms. Then she's swimming!

Don't get her too comfortable though. Overestimating her abilities is 10x worse than a fear of water.

Wait for the hottest day of the year. Get her in the shallow end of the pool with arm and leg floats. Make sure she has properl use of goggles. Let her practice breathing face down into the cool water.
Let her go at her own pace, swimming is a self adjusting learning curve.
My mother used to be an adequate swimmer, but at 89 she just doesn't have the strength or courage to get in the water. She gives me this cute excuse: The others in her senior community pee in the pool and she just doesn't want to swim in that kind of water.