Lighter spaces and mobile families have spawned a new way of thinking about furniture design. Whether you live in a one-bedroom apartment, a townhouse or a spacious single family home, there are good reasons for finding furniture that solves problems -- from ease of moving and setting up to the need for multiple functions. The pieces shown on these pages were designed to be flexible, to fold up, disappear, grow with your needs. Roughly, they fall into four categories -- tables of every imaginable type from the Colonial period to today, chairs, beds and storage systems. CAPTION: Picture 1, Alexandria designer Peter Danko's classic glass table, of hand-hewn tubes of oak and glass slabs. The table is effective in a small space because one sees through it.This one measures 4 feet by 4 feet and costs $850; available at The Pond Gallery, Alexandria.; Picture 2, We've all got a folding card table in the closet for emergencies, but few of us have thought of using a folding table as the main dining table. This handsome design by Mario Bellini is a masterpiece for mobile families. But for $4,180 to $6,180 that's the least you could expect. Available from architects and designers.; Pictures 3 and 4, Ottomans can be transformed into single beds, like this one from Castro Convertible, retailing for $269 with cover shown. The folded-up ottoman is at far left, and the open bed is at left. The ottoman is sold separately from a cover, which is available in a wide range of fabrics and colors.; Picture 5, The classic canvas sling chair has taken on a new look with this design by Gold Medal called Hail Ragnar. A comfortable two-position chair upholstered in canvas, it weighs only 30 pounds and has the advantage of looking appropriate in any living room. A young couple purchasing such a chair would find it adaptable to a growing family until it is relegated to an equally comfortable spot in the recreation room. It sells for $243 (the ottoman is sold separately) and may be purchased from Theodore's or from The Wood Shop.; Pictures 6 and 7, People living in small spaces could hardly afford the room a butcher block table required -- until this clever folding version came on the market. Available from W. Bell & Co. showrooms for $172.75.; Picture 8, Kittinger's revolving tilt-top table measures 27 inches high and 21 1/2 inches in diameter. About $900 from Woodies and Jules Rist Interiors.; Picture 9, The Manhattan group by Rudd International is an unusual storage system with tambour doors. The furniture becomes almost sculptural. Prices from $732 to $1,156, from architects and designers.; Picture 10, There are dozens of folding chairs on the market that fold flat for easy storage, but this one by Castelli is transparent, making it appear to take up even less space. The chair comes in other materials. It boasts a companion table called Plano, which is available in round or square versions on a pedestal base. It's made to fold up into quarters. The chair, called Plia, sells for $75 at Bloomingdale's. Picture 11, Lightweight shelves by Valstrap are made of polypropylene, making it unnecessary to hassle with lining up metal shelf brackets exactly right. The slings here run $16.45 from Hechinger's. The same firm makes stereo strap slings so that you can get those big boxes off the floor and on the wall. The stereo sling is available by mail order only from Valstrap Designs Ltd. New Rochelle, N.Y. 10801.; Pictures 12 and 13, Furniture designed to grow with your needs is this set from Lewis of London, a New York-based franchise. The crib converts to a single bed and the two chests sit on the floor once a crib is no longer needed. The entire set copsts $750, mail-order from Lewis of London, 72-14 Austin St., Forest Hills, N.Y. Similar drawer and bed sets for children are also available in this area.; Picture 14, This handsome "Eta" bookcase, imported by Beylerian from Italy, can be arranged in a variety of configurations. The version shown here costs about $1,235 and is available through interior designers and architects.; Picture 15, Kittinger's classic mahogany dropleaf table is a spacesaver that has been copied and interpreted in a number of forms over the centuries. It sells for $1,120 and measures 43 inches square when both leaves are open.; Picture 16, This large, low coffee table in walnut or ashwood is a great place to store liquor bottles or all those back issues of The Washington Post Magazine you mean to read. Called Il Castello, it's designed by Mario Bellini and imported by Atelier Furniture. The price is $2,620 in ashwood. Available through architects or designers.; Picture 17, Sofa beds are an age-ld space sver, but this one has the advantage of opening to just twice the width you see here, so you no longer have to pull away the coffee table and rearrange the room every time you have a guest over. From Castro Convertibles. Price depends on materials selected. As shown here, about $1,075.; Picture 18, Stack tables have been around since the 19th century in America, but this Italian version by Gianfranco Frattini offers a new twist. Constructed of solid wood with plastic laminate tops, the four individual tables can be stacked into one neat, space-saving and attractive table or stool. Available in a painted or stained finish and imported by Atelier International, the set sells for $965 through architects and designers.