I have to preface this by saying that I am going to strictly stick to the topic of a gastrique (more or less). This will be difficult considering that a gastrique (or gastric) is based upon other main sauces (often called "mother sauces"). I'm assuming that you're more than a beginner cook, and are ready to venture into a more advanced level of culinary creations. If you've never heard of the 5 mother sauces (béchamel, velouté, brown or espagnole, tomato, and hollandaise) then I suggest you start with a different question.
If you are really into making sauces, from appetizers to desserts, then I suggest the following book. You can pick up all 598 pages of awesomeness for under $30, or under $20 if you don't mind a used one. It is well worth the investment and has saved my sorry butt more than once.
Sauces: Classical and Contemporary Sauce Making, by James Peterson
Where to buy:
Without typing word-for-word, Iím going to attempt to summarize what the above book and Professional Cooking, 6th Ed by Wayne Gisslen, have written about gastriques.
A gastrique is a sweet and sour sauce that is usually prepared with a mixture of vinegar (usually wine) to caramelized sugar in a ratio of 2 to 1. A common example of this type of sauce is the classic duck a l'orange. To prepare the gastrique, heat 4 oz (by weight) of granulated sugar in a heavy-bottomed pan over med-low heat. When the sugar is melted and has started to turn pale brown, pour in 1/2 cup of vinegar... I have to diverge here. This is where the book is a little vague, and is open to interpretation. It says "wine" vinegar. Not red. Not white. Not sherry. Just wine. Your best bet? Try it with one type of wine. If you don't like it, dump it out and try again next time. I mean, sugar and vinegar aren't exactly truffles and caviar. Back to our regularly scheduled program... pour in 1/2 cup of vinegar and stand back to avoid splatters. The sugar before adding the vinegar is somewhere in the neighborhood of 300 deg F, and the vinegar boils at 212 deg F. So the instant that the vinegar hits the sugar it will boil and erupt and splatter. Be careful. After all the vinegar has been added and the splattering stops, stir the mixture over low heat until all the sugar is dissolved. Congratulations. You have made a gastrique. Now, what should you do with it? Flavor other sauces, what else. I wouldn't try it straight up because it's super strong. In fact, you just made enough gastrique to flavor about 2 gallons of any sauce. You should use about 2 tbsp of gastrique to about every 1 qt of sauce, or to taste. Remember, you can always add more, but you can't take it back out. So go slow. Why'd we make so much? Well, it's hard to melt very small quantities of sugar, but this should last in the fridge for a couple of weeks.
It can be used in sweet and sour brown sauces, or also added to sauces containing fruit. It's most often used with red meat, duck, and other game. But I'm sure you'll find plenty of uses for it.
Here's a site that talks about gastriques and has a recipe. I make no claims on the quality of the recipe, but Iím sure a web search for "gastrique recipe" will produce some nice experiments to try.
Happy cooking. Don't burn down the house.