we prove that blowing-up will not affect the Turán density. Using various techniques, we determine the Turán density of every $\{1,2\}$-hypergraph in section 4. Remarkably, the Turán densities of $\{1,2\}$-hypergraphs are in the set $$\bigg\{1,\frac{9}{8}, \frac{5}{4}, \frac{3}{2}, \frac{5}{3},
\ldots, 2-\frac{1}{k},\ldots \bigg \}.$$

Among $r$-uniform hypergraphs, $r$-partite hypergraphs have the smallest possible Turán density. Erdős proved that any $r$-uniform hypergraph forbidding the complete $r$-uniform $r$-partite hypergraphs can have at most $O(n^{r-1/\delta})$ edges. We generalize this theorem to non-uniform hypergraphs. A hypergraph is degenerate if it has the smallest possible Turán density. For $r$-uniform hypergraphs, a hypergraph $H$ is degenerate if and only if $H$ is the subgraph of a blow-up of a single edge. Unlike the degenerate $r$-uniform hypergraphs, the degenerate non-uniform hypergraphs are not classified. For non-uniform hypergraphs, chains–one natural extension of a single edge–are degenerate. Additionally, every subgraph of a blow-up of a chain is also degenerate. However, we give an example of a degenerate, non-uniform hypergraph not contained in any blow-up of a chain. This leaves open the question of which non-uniform hypergraphs are degenerate.

In section 6, we consider the suspension of hypergraphs. The suspension of a hypergraph $H$ is a new hypergraph, denoted by $S(H)$, with 