A high-quality, comprehensive product catalog is essential to the success of Product Search engines and shopping sites such as Yahoo! Shopping, Google Product Search or Bing Shopping. But keeping catalogs up-to-date becomes a challenging task, calling for the need of automated techniques. In this paper, we introduce the problem of product synthesis, a key component of catalog creation and maintenance. Given a set of offers advertised by merchants, the goal is to identify new products and add them to the catalog together with their (structured) attributes. A fundamental challenge is the scale of the problem: a Product Search engine receives data from thousands of merchants and millions of products; the product taxonomy contains thousands of categories, where each category comes in a different schema; and merchants use representations for products that are different from the ones used in the catalog of the Product Search engine. We propose a system that provides an end-to-end solution to the product synthesis problem, and includes components for extraction, and addresses issues involved in data extraction from offers, schema reconciliation, and data fusion. We developed a novel and scalable technique for schema matching which leverages knowledge about previously-known instance-level associations between offers and products; and it is trained using automatically created training sets (no manually-labeled data is needed). We present an experimental evaluation of our system using data from Bing Shopping for more than 800K offers, a thousand merchants, and 400 categories. The evaluation confirms that our approach is able to automatically generate a large number of accurate product specifications, and that our schema reconciliation component outperforms state-of-the-art schema matching techniques in terms of precision and recall.