Elastic Search Query: (A or B) and (C or D)

You can use bool and terms query to do this like below:

{    "query": {        "bool": {            "must": [               {                   "terms": {                      "Country": [                         "USA",                         "UK"                      ]                   }               },               {                   "terms": {                      "Expertise": [                         "Botany",                         "Physics"                      ]                   }               }            ]        }    }}

On the other hand you can only use bool query to do this:

{    "query": {        "bool": {            "must": [               {                   "bool": {                       "should": [                          {                              "term": {                                 "Country": {                                    "value": "USA"                                 }                              }                          },                          {                              "term": {                                 "Country": {                                    "value": "UK"                                 }                              }                          }                       ]                   }               },               {                   "bool": {                       "should": [                          {                              "term": {                                 "Expertise": {                                    "value": "Botany"                                 }                              }                          },                          {                              "term": {                                 "Expertise": {                                    "value": "Physics"                                 }                              }                          }                       ]                   }               }            ]        }    }}

But, please look documentation before asking any other question. Maybe, you may find a shorter query.