Jane Austen...
must be the godmother of the Regency genre of romantic fiction. 
Our 'romance' is different from her 'romance' so I hesitate to claim her as mother of the genre.

Her work ranks among the world's greatest literature;
people that would never read a romance novel most certainly will read Jane Austen.

Her few books offer many delights, and a few challenges,
for her language and her characters' manners show without doubt
that two hundred years have passed since the books' writing.

My favourite:  Persuasion

Georgette Heyer...
can with confidence be called the mother of the Regency genre. 
Every one of her books is an individual joy, with characters that charm,
and situations that invoke laughter and provoke sighs of delight.

Among my favourites:
Regency Buck, Frederica, The Grand Sophy and Bath Tangle

Patricia Veryan...
is one of the very best of the Regency writers who began writing in the 1970's. 
Her Sanguinet regency saga is terrific as is her Georgian series, The Golden Chronicles. 
Her characters are real and fresh, her historical detail impeccable. 
Unfortunately most of her books are out of print, but libraries do carry them,
and an out of print search will turn them up.

Start with Love's Duet, or The Lord and the Gypsy, and you'll be hooked.

I prefer traditional Regencies over Regency historical stories so all the modern authors that I list below are writers of what I consider classic or traditional Regencies--in the style of Heyer.

Clare Darcy - a 1970's author whose books are now out of print but well worth searching out.

Deborah Chester - also out of print but worth finding

Jo Beverley and Mary Jo Putney both wrote unforgettable classic Regencies at the beginning of their careers. Those early titles are very difficult to find, but well worth hunting for.

Carla Kelly - has fabulous military heroes and thought-provoking plots

Barbara Metzger - has a light, humorous touch

My Top Ten Regency Favourites

These titles are my very personal choices for top ten Regencies.
They are books I return to again and again just to visit with the characters
and delight in their wonderful stories.
In no particular order:

1. Deirdre and Don Juan by Jo Beverley  1993 Avon Books

2. A Gypsy at Almack's by Chloe Cheshire  1993  Harper Paperbacks

3. Love's Duet by Patricia Veryan   1979  Fawcett Crest

4. Miss Whittier Makes a List by Carla Kelly  1994  Signet Books

5. Frederica by Georgette Heyer  Pan Books  1968; many reissues

6. Persuasion by Jane Austen  first published 1817; many editions available

7. The Rogue's Lady by Marian Devon    1982  Fawcett

8.  Miss Dower's Paragon by Gayle Buck   1993  Signet

9.  The Runaways by Barbara Hazard   1997  Signet

10. Lady Elizabeth's Comet by Sheila Simonson   1985  Walker