Energetic sequel to ''Huckleberry Finn'' is faithful to original, The Further Adventures of Huckleberry Finn, by Greg Matthews. New York: Crown Publishers. 512 pp. $15.95.

Following the success of ''The Adventures of Huckleberry Finn,'' Mark Twain tried to revive the novel's main characters a decade later in ''Tom Sawyer Abroad'' and ''Tom Sawyer, Detective,'' but both books were failures. Now the true sequel to Twain's masterpiece has appeared almost 100 years later in the form of a first novel by, amazingly, a young Australian-born writer named Greg Matthews.

Like Twain, Matthews is a self-taught writer with little formal education. Brought up on a steady diet of TV westerns, he worked for a railroad as a youth but quit at age 25 to take up writing. Now 34, he lives in Lawrence, Kansas, where he is writing a novel about the Civil War. This sequel, like Twain's original, was published in England before it appeared in America.

''The Further Adventures. . .'' begins when Huck is wrongly accused of the murder of Judge Thatcher. Along with the faithful Jim, Huck lights out for the territory, joining the 1849 Gold Rush and encountering on the trail a cast of characters as wily, scabrous, and entertaining as those in Twain's original.

In this sequel Huck and Jim are a little older and a good deal wiser than they were originally. It is refreshing to see them holding their own in a world of grown-up nonsense and bullying, and it is especially gratifying to follow Jim as he slowly and painfully creates a newer, freer self.

In his genius, Twain used a trick which has been the downfall of lesser authors: He showed us everything through the eyes of a child. The same device works here. Even as he matures, Matthews' Huck retains an innocence that blinds him to much of the world's rascality yet which reveals marvels not to be seen by a more jaundiced eye.

The same plot turns which gave Twain's novel its shape are to be found here as well. The numerous deaths, the hairsbreadth escapes, the sudden and forced changes of clothes and identity are part of the incandescent irreality to be found in the Matthews book.

At one point Huck describes the Gold Rush to Jim as a sort of latter-day quest for the Holy Grail, a reminder of that peculiar combination of piety and greed known as the American Dream, to which Twain was keenly attuned.

At the conclusion of this book, the -heroes find themselves embraced enthusiastically by a society which has never seemed able to make up its mind about them, and the only solution is to light out once more. When their ''sivilized'' clothes begin to pinch, Jim wants to visit Africa to see the black kings there, while Huck is eager to go to the South Seas and howl among the cannibals.

Matthews' novel is not the only recent attempt to revive Huck and Jim. In 1970 John Seelye came out with ''The True Adventures of Huckleberry Finn,'' a literal rewrite of the original which attempts to satisfy Twain's critics, especially the ones who objected to the ending of the novel. (Seelye substitutes a despairing, ''realistic'' ending for Twain's high comic one.) Though the story Matthews tells is totally new, he, like Seelye, appropriates Twain's style so skillfully that it is often necessary to remind oneself that one is reading a work of the late 20th century, not the late 19th.

Indeed, from time to time I found it hard not to prefer the pure adventure of Matthews' book to the weighty themes of the original. With sympathy and penetration, Twain examined the greatest social problem this country has experienced, and it goes without saying that an honest novel about slavery isn't always a pretty novel. In ''The Further Adventures,'' the social issues are smaller, and consequently there is more of a focus on pure adventure.

This book makes terrific reading, but it is something more as well: it reintroduces the original to old friends and perhaps to a new audience, as no purely scholarly book could. ''The Adventures of Huckleberry Finn'' is the closest thing we have to a Great American Novel, and Mr. Matthews' faithful, energetic continuation of the tale is an important reminder of that.