I have a database of articles, some of which have several keyword links. I would to create a select statement that gets an article with keyword1 AND keyword1.

CREATE TABLE sqlite_sequence(name,seq);
CREATE TABLE IF NOT EXISTS "keywords" (
	`id`	integer NOT NULL,
	`keyword`	text,
	`authorid`	integer,
	`titleid`	integer,
	PRIMARY KEY(`id` AUTOINCREMENT)
);
CREATE TABLE IF NOT EXISTS "authors" (
	`id`	integer NOT NULL,
	`author`	text,
	`authorid`	integer,
	`titleid`	integer,
	PRIMARY KEY(`id` AUTOINCREMENT)
);
CREATE TABLE IF NOT EXISTS "docs" (
	`id`	INTEGER,
	`authorid`	INTEGER,
	`title`	TEXT,
	`source`	TEXT,
	`pubyear`	INTEGER,
	`notes`	TEXT,
	`filename`	TEXT,
	`issue`	TEXT,
	`titleid`	INTEGER,
	PRIMARY KEY(`id` AUTOINCREMENT)
);

I have a query with an OR but can't seem to get it working with an AND. Of course this doesn't work because a keyword can't be one thing AND another. The logic of how this can work stumps me.

select title,keywords.keyword from docs
join keywords on docs.authorid=keywords.authorid
and docs.titleid=keywords.titleid
where keyword in("Geometry")
or keyword in ("Mathematics")
order by title;

Is it possible to get a query working with keyword1 AND keyword2?

Obviously not. keyword is single attribute of a single row of a single table and cannot have more than one value at a time.

However, you may find all the "stuffs" with keyword1 and then all the same "stuffs" that have keyword2, and then INTERSECT them to find the "common stuffs".

select title 
  from docs
  join keywords 
    on docs.authorid == keywords.authorid
   and docs.titleid == keywords.titleid
 where keyword == 'Geometry'
INTERSECT
select title 
  from docs
  join keywords 
    on docs.authorid == keywords.authorid
   and docs.titleid == keywords.titleid
 where keyword == 'Geometry'
order by title;

NOTE: Fixed Quotes: " is for identifiers, ' is for text strings
NOTE: Fixed keyword in (entry) to keyword == entry

It would probably be perspicacious to normalize your database.

If the tables were normalized (such that the keyword 'Geometry' is the same keyword when attached to title 'Jiggling Ducks' and 'Dumpy frumps'. As in perhaps:

create table keyword
(
    id integer primary key,
    keyword text collate nocase unique
) strict;
create table docs 
(
    id integer primary key,
    authorid INTEGER,
    title TEXT,
    source TEXT,
    pubyear INTEGER,
    notes TEXT,
    filename TEXT,
    issue TEXT,
    titleid INTEGER
);
create table linkage
(
    keyid integer not null references keyword,
    docid integer not null references docs,
    primary key (keyid, docid),
    unique (docid, keyid)
) without rowid;

THen one could use something like:

select *
  from docs
 where id in ( select docid from linkage, keywords where keyid==id and keyword = 'keyword1'
               intersect
               select docid from linkage, keywords where keyid==id and keyword = 'keyword2'
               intersect
               ...
             )
;

I believe I have solved my problem using views.

create temp view geo as select title,keyword from docs,keywords
where keyword like "%Geometry%"
and docs.authorid=keywords.authorid
and docs.titleid=keywords.titleid;
create temp view math as select title,keyword from docs,keywords
where keyword like "%Mathematics%"
and docs.authorid=keywords.authorid
and docs.titleid=keywords.titleid;

Then my query gave me 2 results:

select geo.title,geo.titleid,geo.keyword,math.title,math.titleid,math.keyword from geo,math 
where geo.title=math.title;
title|keyword|title|keyword
Curves of Constant Width|Geometry|Curves of Constant Width|Mathematics
1 Peg in 3 Holes|Geometry|1 Peg in 3 Holes|Mathematics

After checking the DB I'm convinced these are the only titles that have both 'Geometry' AND 'Mathematics' as keywords. What a great day!

Wow, some excellent suggestions here. Thank you all for the inputs. My use of sqlite has been rather simplistic so far, and this was a good exercise for me.