Mapping a set of objects onto another

I'm trying to map a dataset(let's call it Set1) onto another(Set2). The mapping is done by applying an operation to a subset of Set1 and placing the result to an object of Set2. I would like to know how can I structure the classes in an efficient and elegant manner (trying to learn OOP). Code below is working but the initialization order and content of classes is kindof awkward.

interface Operator{
    public void transform(List<String> from, Element to);
}
class Transform{
    public List<String> fromIndex;
    public Integer toIndex;
    Operator op;
    Mapper m;//NICE TO NOT HAVE ref to Mapper
    Transform(List<String> fromIndex, Integer toIndex, Operator op, Mapper m){
        this.fromIndex = fromIndex;
        this.toIndex = toIndex;
        this.op = op;
        this.m = m;
    }
    public void execute(){
        List<String> from = new ArrayList<String>();
        Element to = m.Set2.get(toIndex);
        for(String s : fromIndex){
            from.add(m.Set1.get(s));
        }
        op.transform(from,to);
    }
}
class Mapper{
    Map<String,String> Set1;
    Map<Integer,Element> Set2;
    List<Transform> transforms;
    Mapper(Map<String,String> Set1, Map<Integer,Element> Set2){
        this.Set1= Set1;
        this.Set2= Set2;
    }
    public void setTransforms(List<Transform> transforms){
        this.transforms = transforms;
    }
    public void doMapping(){
        for(Transform t: transforms){
            t.execute();
        }
    }
}

Typical usage scenario, assuming Set1 and Set2 are already filled (Set2 is filled with Elements whose values will be updated):

List<Transform> tList = new ArrayList<Transform>();
Mapper m = new Mapper(Set1,Set2);
tList.add(new Transform(new ArrayList<String>(Arrays.asList("3", "3_")),3,concatStringToInteger,m));
tList.add(new Transform(new ArrayList<String>(Arrays.asList("4", "4_")),4,concatStringToInteger,m));
tList.add(new Transform(new ArrayList<String>(Arrays.asList("22")),22,concatStringToInteger,m));
tList.add(new Transform(new ArrayList<String>(Arrays.asList("24")),24,concatStringToInteger,m));
m.setTransforms(tList);
m.doMapping();

The operators are just some reusable lamba exp. As you can see, Transform needs to hold a ref to mapper and the whole initialization is awkward. This is not a question about functionality (so please ignore any code errors, the code works) but about structuring this in an OOP (and maintaining a degree of generality) manner. Thanks