The brainchild of the BBC, Doctor Who was intended as combination educational and entertaining series for children. In the beginning, historical stories were alternated with science fiction ones, but eventually this was dropped as the sci-fi were far more popular. Great names associated with Doctor Who include Verity Lambert, producer, and Terry Nation, writer and creator of the Daleks. They also attracted famous guest stars.
Many early episodes no longer exist in video form, but all are preserved in audio thanks to fans who taped the episodes as they were broadcast so they could enjoy them again and again.
In the early days of (British) television, drama was done effectively as a filmed play. Hence the long scenes, static speeches and few cutaways. Just like the original Star Trek.

In this section - Transcripts of the episodes up to the end of the Seventh Doctor.
Eventually.
There are rather a lot of them to type up, you know.
'Modern era' transcripts are/were available elsewhere on the Internet.

The Doctor(s):

1. William Hartnell 1963 - 1966
 2. Patrick Troughton 1966 - 1969
 3. Jon Pertwee 1970 - 1974
 4. Tom Baker 1974 - 1981
 5. Peter Davison 1982 - 1984
 6. Colin Baker 1984 - 1986
 7. Sylvester McCoy 1987 - 1989
(8. Paul McGann 1996 movie + audio productions)
 9. Christopher Eccleston 2005
10. David Tennant 2005 - 2009
11. Matt Smith 2010

The Companions:

Jacqueline Hill as Barbara Wright 1963 - 1965
William Russell as Ian Chesterton 1963 - 1965
Carole Ann Ford as Susan Foreman 1963 - 1964
Maureen O'Brien as Vicki 1965
Adrienne Hill as Katarina 1965
Jean Marsh as Sara Kingdom 1965
Peter Purves as Steven Taylor 1965 - 1966
Jackie Lane as Dodo (Dorothea) Chaplet 1966
Anneka Wills as Polly Lopez 1966 - 1967
Michael Craze as Ben Jackson 1966 - 1967
Fraser Hines as Jamie McCrimmon 1966 - 1969
Deborah Watling as Victoria Waterfield 1967 - 1968
Wendy Padbury as Zoe Heriot 1968 - 1969
Caroline John as Liz Shaw 1970
Katy Manning as Jo Grant 1971 -