To find all subsets of the set $\{ \emptyset, 1 \}$, we can list them as follows:

1. $\emptyset$ (the empty set)
2. $\{\emptyset\}$ (the set containing only the empty set)
3. $\{1\}$ (the set containing only the element 1)
4. $\{\emptyset, 1\}$ (the set containing both elements)

Thus, the complete list of subsets is:

1. $\emptyset$
2. $\{\emptyset\}$
3. $\{1\}$
4. $\{\emptyset, 1\}$

If you have any questions or need further details, let me know! Here are some follow-up questions you might consider:

1. What is the concept of a power set?
2. How many subsets does a set with $n$ elements have?
3. Can you explain the significance of the empty set in set theory?
4. What are the properties of subsets?
5. How would you find subsets for a larger set?

Tip: To find subsets of any set, remember that each element can either be included or excluded, leading to $2^n$ possible subsets for a set with $n$ elements.