<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2021-05-20</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001808805</issuerCik>
        <issuerName>ARYA Sciences Acquisition Corp III</issuerName>
        <issuerTradingSymbol>ARYA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001224962</rptOwnerCik>
            <rptOwnerName>PERCEPTIVE ADVISORS LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>51 ASTOR PLACE, 10TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001249675</rptOwnerCik>
            <rptOwnerName>PERCEPTIVE LIFE SCIENCES MASTER FUND LTD</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>51 ASTOR PLACE, 10TH FLOOR</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10003</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <ownerSignature>
        <signatureName>/s/ Joseph Edelman - for Perceptive Advisors LLC, By: Joseph Edelman, its managing member</signatureName>
        <signatureDate>2021-05-24</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Joseph Edelman - for Perceptive Life Sciences Master Fund Ltd, By: Perceptive Advisors LLC, its investment manager, By: Joseph Edelman, its managing member</signatureName>
        <signatureDate>2021-05-24</signatureDate>
    </ownerSignature>
</ownershipDocument>
